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Professor Xuezhong He

Biography

Prof. Xuezhong (Tony) He completed a BSc in Pure Mathematics in 1982 (Ningxia University, China), a MSc in Applied Mathematics in 1987 (Hebei Normal University, China), a PhD in Applied Mathematics in 1995 (Flinders University), and a PhD in Finance in 2001 (the University of Technology, Sydney). Tony worked as an Associated Lecturer from 1982 to 1984 and a Lecturer from 1987 to 1991 with the Department of Mathematics at Ningxia University, China. Between 1989 and 1990, he worked at Flinders University as a Visiting Scholar. Between 1995 and 1997 he was employed as an Associate Lecturer with School of Mathematics and Statistics at the University of Sydney. Tony joined the Finance Discipline Group at UTS Business School, the University of Technology, Sydney, as a Lecturer in 2001, a Senior Lecturer in 2002, an Associate Professor in 2007, and a Professor in 2011.

As a mathematician in his earlier career, Tony has established an international reputation in the field of the theory and application of nonlinear dynamical systems. He has authored/co-authored more than 40 refereed papers in this area, some of which have appeared in prestigious and high quality field journals such as SIAM and IEEE journals, Physica D, Nonlinear Analysis, Journal of Mathematical Analysis and Applications, and Journal of Mathematical Biology.

Tony’s international research profile in areas of financial market modelling, asset pricing with heterogeneous beliefs, and nonlinear economic dynamics is attested by his publications in a number of the leading international journals in economics and econometrics including Journal of Economic Dynamics and Control, Journal of Economic Behavior and Organization, Macroeconomic Dynamics, Journal of Evolutionary Economics, European Journal of Finance, Quantitative Finance, and Computational Economic.

Tony serves as the Co-Editor of the Journal of Economic Dynamics and Control, the associate editor of Journal of Economic Interaction and Coordination, Journal Differential Equations and Dynamical Systems, Discrete Dynamics in Nature and Society, and the reviewer of the Mathematics Review, American Mathematical Society.

Google scholar citation page

Professor, Finance Discipline Group
Associate Member, Advanced Analytics Institute
Associate Member, Centre for Quantum Computation and Intelligent Systems
Core Member, Quantitative Finance Research Centre
BSc (Ningxia), MSc (HBU), PhD (Flinders), PhD (UTS)
Member, Economic Society of Australia
Download CV  (PDF 450 Kb, 2 pages)
Phone
+61 2 9514 7726
Room
CB08.07.13

Research Interests

Financial market modelling, heterogeneous expectations and learning, nonlinear economic dynamics and bounded rationality, behavior finance and asset pricing.

Can supervise: Yes

Derivatives, Financial Economics, Nonlinear Economics, and Investment.

Chapters

Bohm, V., Chiarella, C., He, X. & Huls, T. 2013, 'A homoclinic route to volatility: Dynamics of asset prices under autoregressive forecasting' in Bischi, G.I., Chiarella, C. & Sushko, I. (eds), Global analysis of dynamic models in economics and finance: Essays in honour of Laura Gardini, Springer, Germany, pp. 289-316.
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The article investigates the impact of mean-reverting forecasts in a model of asset pricing with two groups of investors under market clearing. Fundamentalists believe that asset prices follow an exogenous stochastic process, while chartists assume that asset prices follow a stochastic geometric decay process. For high values of mean reversion a period-doubling bifurcation occurs followed by a Neimark-Sacker bifurcation, after which homoclinic points exist inducing chaotic dynamics. Before the occurrence of homoclinic points, all orbits induce significant fluctuations with recurring symmetries and nonvanishing autocorrelations in all time series of prices and returns. After the homoclinic bifurcation, prices and returns follow alternating phases with low fluctuations near the steady state followed by phases with large excursions from the steady state. This shows that nonlinearities of the deterministic model rather than random perturbations are the causes of volatility clustering and of the generation of fat tails. Autocorrelations of prices and returns vanish while those of absolute returns and squared returns persist for high-order lags. Thus, the model is able to reproduce some important empirical market features
He, X. 2013, 'Recent developments in asset pricing with heterogeneous beliefs and adaptive behaviour of financial markets' in Bischi, G.I., Chiarella, C. & Sushko, I. (eds), Global analysis of dynamic models in economics and finance: Essays in honour of Laura Gardini, Springer, Germany, pp. 3-34.
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Heterogeneity and interacting among boundedly rational agents have received increasing attention in the finance and economics literature. Recent developments on the role of heterogeneous beliefs on asset pricing and the adaptive behaviour of financial markets shed light into the complex behaviour of financial markets and provide some explanations of certain market behaviour and anomalies. This paper surveys these developments, to which the author and several coauthors have contributed in several papers, and discusses the extent to which they can address market anomalies, complexity, and stylized facts in financial markets.
He, X. & Shi, L. 2011, 'Diversification effect of heterogeneous beliefs' in Dawid, H. & Semmler, W. (eds), Computational Methods in Economic Dynamics, Springer, US, pp. 57-75.
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Within the framework of Chiarella et al (2009b) on MV analysis, this paper examines the impact of the heterogeneity and bounded rationality on the market equilibrium and MV efficiency of the optimal portfolios. The heterogeneity is characterised by the heterogeneous beliefs about the returns of the risky assets, while the bounded rationality corresponds to the MV optimisation of investors based on their beliefs.
He, X. & Shi, L. 2010, 'Portfolio efficiency under heterogeneous beliefs' in Kijima, M., Hara, C., Tanaka, K. & Muromachi, Y. (eds), Recent Advances in Financial Engineering, World Scientific, Singapore, pp. 127-156.
In the standard mean variance (MV) capital asset pricing model (CAPM) with homogeneous beliefs, the optimal portfolios of investors are MV efficient. It is expected that this is no longer true in general when investors have heterogeneous beliefs in the means. and variances/covariances of asset returns. This paper extends the s.tandard Black's zero-beta CAPM to incorporate heterogeneous beliefs and verifies that lhe subjectively optima) portfolios of heterogeneous investors are MV inefficient in generaL The paper then demonstrates that the traditional geometric relation of the mean variance frontiers with and Without the riskless asset under homogeneous beliefs does not hold in general under heterogelleous beliefs. The paper further examines the impact of biased beliefs among investors on the MY efficiency of their optimal portfolios. The results provide some explanalions on the risk premium puzzle, Miller's hypothesis, and underperfonnance of managed funds.
Chiarella, C., Dieci, R. & He, X. 2009, 'Heterogeneity, market mechanisms and asset price dynamics' in Hens, T. & Schenk-Hoppe, K.R. (eds), Handbook of Financial Markets: Dynamics and Evolution, Elsevier, USA, pp. 277-344.
He, X., Hamill, P. & Li, Y. 2008, 'Can Trend Followers Survive in the Long-Run? Insights from Agent-Based Modeling' in Brabazon, A. & O'Neill, M. (eds), Natural Computing in Computational Finance, Springer, Berlin, Germany, pp. 253-269.
This chapter uses a simple stochastic market fraction (MF) asset pricing model to investigate market dominance, profitability, and how traders adopting fundamental analysis or trend following strategies can survive under various market conditions in the long/shoft-run. This contrasts with the modern theory of finance which relies on the paradigm of utility maximizing representative agents and rational expectations assumptions which some contemporary theorists regard as extreme. This school of thought would predict that trend followers will be driven out of the markets in the long-run. Our analysis shows that in a MF framework this is not necessarily the case and that trend followers can survive in the long-run.
Chiarella, C. & He, X. 2008, 'An adaptive model of asset price and wealth dynamics in a market with heterogeneous trading strategies' in Seese, D., Weinhardt, C. & Schlottmann, F. (eds), Handbook on Information Technology in Finance, Springer, Germany, pp. 465-499.
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The traditional asset-pricing models such as the capital asset pricing model (CAPM) of [42] and [34], the arbitrage pricing theory (APT) of [40], or the intertemporal capital asset pricing model (ICAPM) of [38] have as one of their important assumptions, investor homogeneity. In particular the paradigm of the representative agent assumes that all agents are homogeneous with regard to their preferences, their expectations and their investment strategies.1 However, as already argued by Keynes in the 1930s, agents do not have sufficient knowledge of the structure of the economy to form correct mathematical expectations that would be held by all agents
Chiarella, C., He, X. & Wang, D. 2006, 'Statistical properties of a heterogeneous asset pricing model with time-varying second moment' in Namatame, A., Kaizouji, T. & Aruka, Y. (eds), The Complex Networks of Economic Interactions: essays in agent-based economics & econophysics, Springer, Berlin, Germany, pp. 109-123.
Chiarella, C., Flaschel, P., He, X. & Hung, H. 2006, 'A stochastic model of real-financial interaction with boundedly rational heterogeneous agents' in Chiarella, C., Franke, R., Flaschel, P. & Semmler, W. (eds), Quantitative and Empirical Analysis of Nonlinear Dynamic Macromodels, Elsevier, Amsterdam, Netherlands, pp. 333-358.
Chiarella, C. & He, X. 2005, 'An asset pricing model with adaptive heterogeneous agents and wealth effects' in Lux, T., Reitz, S. & Samanidou, E. (eds), Nonlinear Dynamics and Heterogeneous Interacting Agents, Springer, Berlin, Germany, pp. 269-285.
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The characterisation of agents' preferences by decreasing absolute risk aversion (DARA) and constant relative risk aversion (CRRA) are well documented in the literature and also supported in both empirical and experimental studies. This paper considers a financial market with heterogeneous agents having power utility functions, which are the only utility functions displaying both DARA and CRRA. By introducing a population weighted average wealth measure, we develop an adaptive model to characterise asset price dynamics as well as the evolution of population proportions and wealth dynamics. Some numerical simulations are included to illustrate the evolution of the wealth dynamics, market behaviour and market efficiency within the framework of heterogeneous agents.
Chiarella, C. & He, X.Z. 2004, 'Dynamics of beliefs and learning under a(L)-processes - The homogeneous case', pp. 363-390.
Chiarella, C. & He, X. 2000, 'The dynamics of the cobweb when producers are risk averse learners' in Hartl, E.J., Dockner, R.F., Luptacik, M. & Sorger, G. (eds), Optimization, Dynamics, and Economic Analysis, Physica-Verlag, Heidelberg, Germany, pp. 86-100.

Conferences

He, X. 2013, 'Asset pricing under keeping up with the Joneses and heterogeneous beliefs'.
He, X. & Shi, L. 2012, 'Asset pricing under keeping up with the Joneses and heterogeneous beliefs'.
Chiarella, C., Dieci, R. & He, X. 2012, 'Time-varying beta: A boundedly rational equilibrium approach'.
Chiarella, C., Dieci, R. & He, X. 2012, 'Heterogeneity, market mechanisms, and asset price dynamics'.
He, X. 2012, 'Recent developments in asset pricing with heterogeneous beliefs and adaptive behaviour of financial markets'.
He, X. & Treich, N. 2012, 'Heterogeneous beliefs and prediction market accuracy'.
He, X., Shi, L. & Zheng, M. 2012, 'Asset pricing under keeping up with the Joneses and heterogeneous beliefs'.
Bohm, V., Chiarella, C., He, X. & Huls, T. 2012, 'A homoclinic route to volatility: Dynamics of asset prices under autoregressive forecasting'.
Chiarella, C., Dieci, R., He, X. & Li, K. 2012, 'An evolutionary CAPM under heterogeneous beliefs', Proceedings of the 25th Australasian Finance and Banking Conference 2012, University of NSW, Sydney, Australia, pp. 1-38.
He, X. 2011, 'Dynamics of a continuous-time financial market model with heterogeneous beliefs'.
Chiarella, C., Dieci, R. & He, X. 2011, 'Time-varying beta: A boundedly rational equilibrium approach'.
He, X. 2011, 'Heterogeneity, market mechanisms, and asset price dynamics'.
He, X. 2011, 'Market efficiency and moving average rules in financial markets'.
He, X. & Shi, L. 2011, 'Asset pricing under keeping up with the Joneses and heterogeneous beliefs'.
He, X. & Shi, L. 2011, 'Heterogeneous beliefs and the dynamics of cross-sectional asset returns'.
He, X. & Li, K. 2011, 'Contrarian, momentum, and market stability'.
He, X. 2011, 'Heterogeneous beliefs and adaptive behaviour of financial market: Recent development and challenge'.
Chiarella, C., He, X. & Zheng, M. 2010, 'The market impact and survival of boundedly rational traders'.
He, X. & Zheng, M. 2010, 'Dynamics of moving average rules in a continuous-time financial market model'.
He, X. & Li, Y. 2010, 'Market maker, stability and power-law behaviour'.
He, X. & Shi, L. 2010, 'Differences in opinion and risk premium'.
He, X. 2010, 'A model of financial market with delay'.
Chiarella, C., He, X. & Zheng, M. 2009, 'Consensus investor and intertemporal asset pricing with heterogeneous beliefs'.
Chiarella, C., Dieci, R. & He, X. 2009, 'Time-varying beta: A bounded rational equlibrium approach'.
Chiarella, C., Dieci, R. & He, X. 2009, 'Time-varying beta: A bounded rational equilibrium approach'.
He, X. & Shi, L. 2009, 'Bounded rational equilibrium and risk premium'.
He, X. 2009, 'Does the market maker stabilize the market?'.
He, X. & Zheng, M. 2009, 'Dynamics of moving average rules in a continuous-time financial market model'.
Bohm, V., Chiarella, C. & He, X. 2008, 'Dynamics of asset prices in the CAPM under autoregressive forecasting and noise'.
Chiarella, C., He, X. & Zheng, M. 2008, 'Consensus investor and intertemporal asset pricing with heterogeneous beliefs'.
Chiarella, C., He, X. & Zheng, M. 2008, 'The stochastic dynamics of speculative prices'.
Chiarella, C., Dieci, R. & He, X. 2008, 'Heterogeneity, market mechanisms and asset price dynamics'.
Chiarella, C., He, X. & Zheng, M. 2008, 'Heterogeneous expectations and exchange rate dynamics'.
He, X. & Shi, L. 2008, 'Zero-beta heterogeneous CAPM'.
He, X. & Shi, L. 2008, 'Heterogeneity, bounded rationality and market dysfunctionality'.
Chiarella, C., Dieci, R. & He, X. 2008, 'A dynamic heterogeneous beliefs CAPM'.
Chiarella, C., He, X., Wang, D. & Zhu, M. 2008, 'Stock price and market maker inventory dynamics with heterogeneous beliefs'.
He, X. & Li, Y. 2008, 'Calibrating a market fraction model to the power-law behaviour in the DAX'.
He, X. & Shi, L. 2008, 'Zero-beta CAPM with heterogeneous beliefs'.
He, X. & Shi, L. 2008, 'Portfolio analysis and zero-beta heterogeneous CAPM'.
He, X. 2008, 'Heterogeneous expectations and exchange rate dynamics'.
Chiarella, C., He, X. & Zheng, M. 2007, 'The stochastic price dynamics of speculative behaviour'.
He, X. 2007, 'The stochastic bifurcation of a speculative asset pricing model'.
He, X. 2007, 'Aggregation of heterogeneity beliefs and asset pricing theory: A mean-variance analysis'.
He, X. 2007, 'Aggregation of heterogeneity beliefs and asset pricing theory: A mean variance analysis'.
Chiarella, C., Dieci, R. & He, X. 2007, 'Aggregation of heterogeneous beliefs and asset pricing theory: A mean-variance analysis'.
He, X. 2007, 'Heterogeneity, bounded rationality, and market dysfunctionality'.
He, X. & Shi, L. 2007, 'Zero-beta CAPM with heterogeneous beliefs'.
Chiarella, C., Dieci, R. & He, X. 2006, 'A dynamic heterogenous beliefs CAPM', Complex Behavior in Economics: Modelling, Computing and Mastering Complexity, GREQAM, Aix-en-Provence, France, pp. 1-26.
Chiarella, C., Dieci, R. & He, X. 2006, 'A dynamic heterogenous beliefs CAPM'.
Chiarella, C., Dieci, R. & He, X. 2006, 'Aggregation of heterogenous beliefs and asset pricing: A mean-variance analysis'.
Chiarella, C., Dieci, R. & He, X. 2006, 'Aggregation of heterogeneous beliefs and asset pricing: A mean-variance analysis.'.
Chiarella, C., Dieci, R. & He, X. 2006, 'On the dynamic behavior of asset prices in disequilibrium: Where are we after three decades?'.
Chiarella, C., Dieci, R. & He, X. 2006, 'On the dynamic behaviour of asset prices in disequilibrium: Where are we after three decades?'.
Chiarella, C., He, X. & Li, Y. 2006, 'A dynamic heterogenous beliefs CAPM'.
He, X. & Li, Y. 2006, 'Long memory, heterogeneity and trend chasing', 17th Annual Asian Finance Association/ FMA Conference, Asian Finance Association, Auckland, New Zealand, pp. 1-33.
Chiarella, C., Bohm, V. & He, X. 2005, 'The interaction of non-linear and stochastic elements in a one period model of asset price dynamics', Econophysics Colloquium, -, -.
He, X. 2005, 'Heterogeneity, profitability and autocorrelations', 2005 Global Finance Conference, -, -.
He, X. 2005, 'Heterogeneity, profitability and autocorrelations', Quantitative Methods in Finance 2005 Conference, -, -.
He, X. & Li, Y. 2005, 'Heterogeneity, profitability and autocorrelations', Proceedings of the 11th Annual Conference on Computing in Economics and Finance, University of Maryland, Washington, USA, pp. 1-44.
He, X. & Li, Y. 2005, 'Long memory, heterogeneity and trend chasing', Proceedings of the Australian Conference of Economists 2005, Economic Society of Australia, Melbourne, Australia, pp. 1-31.
Bird, R., He, X., Thosar, S.B. & Woolley, P.K. 2004, 'The case for market inefficiency: Investment style and market pricing', 2004 Financial Management Association Meeting, Financial Management Association, USA, pp. 1-24.
Chiarella, C., Flaschel, P., He, X. & Hung, H. 2004, 'A stochastic model of real-financial interaction with boundedly rational heterogeneous agents', Society for nonlinear dynamics and economics, -, -.
Chiarella, C., He, X. & Hommes, C. 2004, 'A dynamic analysis of moving average rules', Computational Economics - 10th International Conference on Computing in Economics and Finance, Society for Computational Economics, Amsterdam, pp. 1-19.
He, X. 2004, 'Economic dynamics asset pricing and nonlinear adaptive evolutionary systems', International Conference on Nonlinear Dynamics and Evolution Equations, -, -.
Chiarella, C. & He, X. 2003, 'Asset pricing and wealth dynamics - an adaptive model with heterogenous agents', WEHIA 2003, Institute of Economics, Keil, pp. 1-20.
Chiarella, C., Flaschel, P., He, X. & Hung, H. 2003, 'A stochastic model of real-financial interaction with boundedly rational heterogeneous agents', Bielefeld Workshop on Real-Financial Interaction, --, --.
Chiarella, C. & He, X. 2003, 'An adaptive model of asset pricing and wealth dynamics with heterogeneous trading strategies', WEHIA 2003 - Annual Workshop on Economics with Heterogeneous Interacting Agents, --, --.
Chiarella, C., He, X. & Zhu, P. 2003, 'Fading memory learning in the cobweb model with risk averse heterogeneous producers', 9th International Conference on Computing in Economics and Finance, --, --.
He, X. 2003, 'Asset pricing volatility and market behaviour: a market fraction approach', Quantitative Methods in Finance 2003 Conference, --, --.
He, X. 2002, 'Adaptiveness, wealth dynamics and asset pricing with heterogeneous agents', Quantitative Methods in Finance 2002 Conference.
Chiarella, C. & He, X. 2002, 'Adaptive models of asset pricing and wealth dynamics in economies with heterogeneous agents', Workshop on Economic Dynamics - CENDEF.
Chiarella, C. & He, X. 2002, 'An adaptive model on asset pricing and wealth dynamics with heterogeneous trading systems', Asia Pacific Finance Association Conference.

Journal articles

Chiarella, C., He, X. & Zheng, M. 2013, 'Heterogeneous expectations and exchange rate dynamics', The European Journal of Finance, vol. 19, no. 5, pp. 392-419.
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This article presents a continuous-time model of exchange rates not only relying on macroeconomic factors but also having an investor heterogeneity component. The driving macroeconomic factor is the domesticforeign interest rate differential, while the investor heterogeneity is described by the expectations of boundedly rational portfolio managers who use a weighted average of the expectations of fundamentalists and chartists. Within this framework, the different roles of the macroeconomic factor and investor heterogeneity in the determination of the exchange rate are examined explicitly. We show that this simple model generates very complicated market behaviour, including the existence of multiple steady-state equilibria, deviations of the market exchange rate from the fundamental one and market fluctuations. Numerical simulation of the corresponding stochastic version of the model shows that the model is able to generate typical time series and volatility clustering patterns observed in exchange rate markets.
Chiarella, C., Dieci, R. & He, X. 2013, 'Time-varying beta: A boundedly rational equlibrium approach', Journal of Evolutionary Economics, vol. 23, no. 3, pp. 609-639.
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The conditional CAPM with time-varying betas has been widely used to explain the cross-section of asset returns. However, most of the literature on time-varying beta is motivated by econometric estimation using various latent risk factors rather than explicit modelling of the stochastic behaviour of betas through agents behaviour, such as momentum trading. Misspecification of beta risk and the lack of any theoretical guidance on how to specify risk factors based on the representative agent economy appear empirically challenging. In this paper, we set up a dynamic equilibrium model of a financial market with boundedly rational and heterogeneous agents within the mean-variance framework of repeated one-period optimisation and develop an explicit dynamic behaviour CAPM relation between the expected equilibrium returns and time-varying betas. By incorporating the two most commonly used types of investors, fundamentalists and chartists, into the model, we show that there is a systematic change in the market portfolio, risk-return relationships, and time varying betas when investors change their behaviour, such as the chartists acting as momentum traders. In particular, we demonstrate the stochastic nature of time-varying betas. We also show that the commonly used rolling window estimates of time-varying betas may not be consistent with the ex-ante betas implied by the equilibrium model. The results provide a number of insights into an understanding of time-varying beta.
Chiarella, C., Dieci, R., He, X. & Li, K. 2013, 'An evolutionary CAPM under heterogeneous beliefs', Annals of Finance, vol. 9, no. 2, pp. 185-215.
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Heterogeneity and evolutionary behaviour of investors are two of the most important characteristics of financial markets. This paper incorporates the adaptive behaviour of agents with heterogeneous beliefs and establishes an evolutionary capital asset pricing model (ECAPM) within the mean-variance framework. We show that the rational behaviour of agents switching to better-performing trading strategies can cause large deviations of the market price from the fundamental value of one asset to spill over to other assets. Also, this spill-over effect is associated with high trading volumes and persistent volatility characterized by significantly decaying autocorrelations of, and positive correlation between, price volatility and trading volume.
Di Guilmi, C., He, X.-.Z. & Li, K. 2013, 'Herding, trend chasing and market volatility', Journal of Economic Dynamics and Control.
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We introduce a heterogeneous agent asset pricing model in continuous-time to show that, although trend chasing, switching and herding all contribute to market volatility in price and return and to volatility clustering, their impacts are different. The fluctuations of the market price and return and the level of the significant autocorrelations (ACs) of the absolute and squared returns increase with the intensities of herding and trend chasing based on long time horizon. However an increase in switching intensity reduces the return volatility and in particular a low switching intensity reduces the price volatility and increases the level of the significant ACs, but the effect becomes opposite when the switching intensity is high. We also show that market noise plays a more important role than fundamental noise on the power-law behavior of returns. 2014 Elsevier B.V.
He, X. & Shi, L. 2012, 'Boundedly rational equilibrium and risk premium', Accounting and Finance, vol. 52, no. 1, pp. 71-93.
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When people agree to disagree, the impact of the disagreement among agents on the market is the main concern of this paper. With the standard mean variance framework, this paper considers a market of two risky assets and two agents who have different preference and disagreement about the mean and variance/covariance of the asset returns. By constructing a consensus belief, the paper develops an concept of boundedly rational equilibrium (BRE) to characterize the market equilibrium and examines explicitly the impact of heterogeneity on the market equilibrium and risk premium when the disagreements among the two agents are mean preserved spreads of a benchmark homogeneous belief. It shows that, in market equilibrium, the biased mean preserved spreads in beliefs among the two agents have significant impact on the risk premium of the risky assets and market portfolio, and adding a riskless asset in the market magnifies the impact of the heterogeneity on the market. The results show that both optimism/pessemism and confidence/doubt can increase the market risk premium and reduce the riskfree rate.
He, X. & Shi, L. 2012, 'Disagreement, correlation and asset prices', Economics Letters, vol. 116, no. 3, pp. 512-515.
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When people agree to disagree, how does the disagreement affect asset prices? Within an equilibrium framework with two agents, two risky assets and a riskless bond, we analyze the joint impact of disagreement about expected payoff, variance and correlation, and compare prices with benchmark prices in a market with homogeneous beliefs.
Chiarella, C., He, X. & Pellizzari, P. 2012, 'A dynamic analysis of the microstructure of moving average rules in a double auction market', Macroeconomic Dynamics, vol. 16, no. 4, pp. 556-575.
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Inspired by the theoretically oriented dynamic analysis of moving average rules in the model of Chiarella, He, and Hommes (CHH) [Journal of Economic Dynamics and Control 30 (2006), 1729-1753], this paper conducts a dynamic analysis of a more realistic microstructure model of continuous double auctions in which the probability of heterogeneous agents trading is determined by the rules of either fundamentalists mean-reverting to the fundamental or chartists choosing moving average rules based on their relative performance. With such a realistic market microstructure, the model is able not only to obtain the results of the CHH model but also to characterize most of the stylized facts including volatility clustering, insignificant autocorrelations (ACs) of returns, and significant slowly decaying ACs of the absolute returns. The results seem to suggest that a comprehensive explanation of several statistical properties of returns is possible in a framework where both behavioral traits and realistic microstructure have a role
He, X. & Shi, L. 2012, 'Disagreement in a multi-asset market', International Review of Finance, vol. 12, no. 3, pp. 357-373.
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This paper provides a simple framework to study the effect of disagreement in a multi-asset market equilibrium by considering two agents who disagree about expected returns, variances, and correlation of returns of two risky assets. When agents' subjective beliefs are characterized by mean preserving spreads of a benchmark homogeneous belief, we show that the effect of the disagreement does not cancel out in general and the effect in a multi-asset market can be very different from a single asset market. In particular, the market risk premium can increase and the risk-free rate can decrease significantly even when the market is overoptimistic and overconfident.
He, X. & Li, K. 2012, 'Heterogeneous beliefs and adaptivebehaviour in a continuous-time asset price model', Journal of Economic Dynamics and Control, vol. 36, no. 7, pp. 973-987.
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This paper extends the analysis of the seminal work of . Brock and Hommes (1997, 1998) on heterogeneous beliefs and rational routes to randomness in discrete-time models to a continuous-time model of asset pricing. The resulting model characterised mathematically by a system of stochastic delay differential equations provides a unified approach to deal with adaptive behaviour of heterogeneous agents and market stability impact of lagged price used by chartists to form their expectations. For the underlying deterministic model, we show not only that the result of Brock and Hommes on rational routes to market instability in discrete-time holds in continuous-time but also a double edged effect of an increase in lagged price used by the chartists on market stability. For the stochastic model, we demonstrate that the interaction and boundedly rational behaviour of heterogeneous agents can generate various market phenomena such as bubbles and crashes and replicate stylised facts including volatility clustering, and long range dependence in volatility.
Chiarella, C., Dieci, R. & He, X. 2011, 'The dynamic behaviour of asset prices in disequilibrium: a survey', International Journal of Behavioural Accounting and Finance, vol. 2, no. 2, pp. 101-139.
This article surveys boundedly rational heterogeneous agent (BRHA) models of financial markets. We give particular emphasis to the role of the market clearing mechanism used, the utility function of the investors, the interaction of price and wealth dynamics, and calibration of this class of models. Due to agents behavioural features and market noise, the BRHA class of models are both non-linear and stochastic. We show that BRHA models produce both a locally stable fundamental equilibrium corresponding to that of the standard paradigm, as well as instability with a consequent rich range of possible complex behaviours that are analysed by both simulation and deterministic bifurcation analysis. A calibrated model is able to reproduce quite well the stylised facts of financial markets. The BRHA framework seems able to better accommodate market features such as fat tails, volatility clustering, large excursions from the fundamental and bubbles than the standard financial market paradigm.
He, X. & Zheng, M. 2010, 'Dynamics of moving average rules in continuous-time financial market model', Journal of Economic Behavior & Organization, vol. 76, no. 3, pp. 615-634.
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Within a continuous-time framework, this paper proposes a stochastic heterogeneous agent model (HAM) of financial markets with time delays to unify various moving average rules used in discrete-time HAMs. The time delay represents a memory length of a moving average rule in discrete-time HAMs. Intuitive conditions for the stability of the fundamental price of the deterministic model in terms of agents behavior parameters and memory length are obtained. It is found that an increase in memory length not only can destabilize the market price, resulting in oscillatory market price characterized by a Hopf bifurcation, but also can stabilize an otherwise unstable market price, leading to stability switching as the memory length increases. Numerical simulations show that the stochastic model is able to characterize long deviations of the market price from its fundamental price and excess volatility and generate most of the stylized facts observed in financial markets.
He, X., Li, K., Wei, J. & Zheng, M. 2009, 'Market stability switches in a continuous-time financial market with heterogeneous beliefs', Economic Modelling, vol. 26, no. 6, pp. 1432-1442.
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By considering a financial market of fundamentalists and trend followers in which the price trend of trend followers is formed as a weighted average of historical prices, we establish a continuous-time financial market model with time delay and examine the impact of time delay on market price dynamics. Conditions for the stability of the fundamental price in terms of agents' behavior parameters and time delay are obtained. In particular, it is found that an increase in time delay can not only destabilize the market price but also stabilize an otherwise unstable market price, leading to stability switching as delay increases. These interesting phenomena shed new light in understanding of mechanism on the market stability. When the fundamental price becomes unstable through Hopf bifurcations, sufficient conditions on the stability and global existence of the periodic solution are obtained.
Zheng, M., Wang, D. & He, X. 2009, 'Asymmetry of technical analysis and market price volatility', China Finance Review, vol. 61, no. 2, pp. 61-89.
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He, X.-.Z. & Li, Y. 2008, 'Heterogeneity, convergence, and autocorrelations', Quantitative Finance, vol. 8, no. 1, pp. 59-79.
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This paper is a contribution to the literature on the explanatory power and calibration of heterogeneous asset pricing models. We set out a new stochastic market-fraction asset pricing model of fundamentalists and trend followers under a market maker. Our model explains key features of financial market behaviour such as market dominance, convergence to the fundamental price and under- and over-reaction. We use the dynamics of the underlying deterministic system to characterize these features and statistical properties, including convergence of the limiting distribution and autocorrelation structure. We confirm these properties using Monte Carlo simulations.
Gong, G., Gao, J. & He, X. 2008, 'Exchange Rate Regime and Monetary Policy: A Proposal for Small and Less Developed Economies', Jingji Yanjiu - Economic Research Journal, vol. 43, no. 6, pp. 25-36.
He, X.-.Z. & Li, Y. 2007, 'Power-law behaviour, heterogeneity, and trend chasing', Journal of Economic Dynamics and Control, vol. 31, no. 10, pp. 3396-3426.
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Long-range dependence in volatility is one of the most prominent examples in financial market research involving universal power laws. Its characterization has recently spurred attempts to provide some explanations of the underlying mechanism. This paper contributes to this recent line of research by analyzing a simple market fraction asset pricing model with two types of traders - fundamentalists who trade on the price deviation from estimated fundamental value and trend followers whose conditional mean and variance of the trend are updated through a geometric learning process. Our analysis shows that agent heterogeneity, risk-adjusted trend chasing through the geometric learning process, and the interplay of noisy fundamental and demand processes and the underlying deterministic dynamics can be the source of power-law distributed fluctuations. In particular, the noisy demand plays an important role in the generation of insignificant autocorrelations (ACs) on returns, while the significant decaying AC patterns of the absolute returns and squared returns are more influenced by the noisy fundamental process. A statistical analysis based on Monte Carlo simulations is conducted to characterize the decay rate. Realistic estimates of the power-law decay indices and the (FI)GARCH parameters are presented. 2007 Elsevier B.V. All rights reserved.
Corron, N., He, X. & Westerhoff, F.H. 2007, 'Butter Mountains, Milk Lakes and optimal Price Limiters', Applied Economic Letters, vol. 14, no. 15, pp. 1131-1136.
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It is known that simple price limiters may have unexpected consequences in irregular commodity price fluctuations between bull and bear markets and complicated impacts on the size of buffer stocks. In particular, imposing a lower price boundary may lead to a huge buffer stock, e.g. to a ?butter mountain? or a ?milk lake? and this is a real problem for regulators since storage costs may become impossible to finance over time. The relation between price limiters and the size of buffer stocks is nontrivial and there may exist some optimal price limiters which require only weak market interventions and thus provide a rather inexpensive option to regulate commodity markets. In this article, we use a simple commodity market model to explore the relation between price limiters and the average growth rate of the buffer stocks. It is found that these optimal price limiter levels are simply the minimum values of unstable periodic orbits of the underlying deterministic system.
Chiarella, C., Dieci, R. & He, X. 2007, 'Heterogeneous Expectations and Speculative Behavior in a Dynamic Multi-Asset Framework', Journal of Economic Behavior and Organization, vol. 62, no. 3, pp. 408-427.
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This paper develops a dynamic model of a financial market where heterogeneous agents invest among multiple risky assets and a risk-free asset, under a market maker scenario. Particular attention is paid to the case of two risky assets and two agent types, fundamentalists and trend chasers, whose beliefs on both first and second moments of the conditional distribution of returns are based on past observations. Conditions for the stability of the ?fundamental? equilibrium are established and the effect of the correlation between the risky assets is examined. It turns out that investors? anticipated correlation and dynamic portfolio diversification do not always have a stabilizing role, but rather may act as a source of complexity in the financial market.
Chiarella, C., He, X.Z. & Wang, D. 2006, 'A behavioral asset pricing model with a time-varying second moment', CHAOS SOLITONS & FRACTALS, vol. 29, no. 3, pp. 535-555.
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Dieci, R., Foroni, I., Gardini, L. & He, X. 2006, 'Market mood, adaptive beliefs and asset price dynamics', Chaos, Solitons and Fractals, vol. 29, no. 3, pp. 520-534.
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Empirical evidence has suggested that, facing different trading strategies and complicated decision, the proportions of agents relying on particular strategies may stay at constant level or vary over time. This paper presents a simple dynamic market frac
Ruan, D. & He, X. 2006, 'Global Stability In Chemostat-type Competition Models With Nutrient Recycling (vol 58, Pg 170, 1998)', Siam Journal On Applied Mathematics, vol. 66, no. 6, pp. 2204-2205.
This note corrects some typos and errors in the paper [S. Ruan and X.-Z. He, SIAM J. Appl. Math., 58 (1998), pp. 170-192].
Chiarella, C., He, X. & Hommes, C. 2006, 'A dynamic analysis of moving average rules', Journal of Economic Dynamics and Control, vol. 30, no. 9-10, pp. 1729-1753.
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The use of various moving average (MA) rules remains popular with financial market practitioners. These rules have recently become the focus of a number empirical studies, but there have been very few studies of financial market models where some agents
He, X. & Westerhoff, F.H. 2005, 'Commodity markets, price limiters and speculative price dynamics', Journal Of Economic Dynamics & Control, vol. 29, no. 9, pp. 1577-1596.
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We develop a behavioral commodity market model with consumers, producers and heterogeneous speculators to characterize the nature of commodity price fluctuations and to explore the effectiveness of price stabilization schemes. Within our model, we analyz
Bird, R., He, X., Thosar, S.B. & Woolley, P.K. 2005, 'The case for market inefficiency: investment style and market pricing', The Journal of Asset Management, vol. 5, no. 6, pp. 365-388.
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The level of informational efficiency of security markets has been a contentious issue among the academic and broader community over the last 35 years. This study highlights the growth in popularity in investment styles over this period, where investment decisions are made with only limited reference to available information and no concern with fair value (eg momentum investors and index investors). This paper models the market behaviour of fundamental, momentum and index investors and then simulates the behaviour of security prices in a market composed of investors following these three styles. Evidence is found to suggest that compositions of investment styles that are fairly typical of the mix of investors in current-day markets will lead to anomalous price behaviour similar to that found by other writers: an underreaction to new information which often gives rise to a subsequent overreaction
Bird, R., He, X., Thosar, S.B. & Woolley, P.K. 2005, 'Momentum and index investing: implications for market efficiency', Journal of Financial Transformation, vol. 15, no. December, pp. 79-85.
Chiarella, C. & He, X. 2003, 'Heterogeneous beliefs, risk, and learning in a simple asset-pricing model with a market maker', Macroeconomic Dynamics, vol. 7, no. 4, pp. 503-536.
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Chiarella, C. & He, X.Z. 2003, 'Dynamics of beliefs and learning under a(L)-processes - the heterogeneous case', JOURNAL OF ECONOMIC DYNAMICS & CONTROL, vol. 27, no. 3, pp. 503-531.
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Chiarella, C. & He, X. 2002, 'Heterogeneous beliefs, risk and learning in a simple asset pricing model', Computational Economics, vol. 19, no. 1, pp. 95-132.
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Chiarella, C. & He, X. 2001, 'Asset Price & Wealth Dynamics Under Heterogeneous Expectations', Quantitative Finance, vol. 1, no. 5, pp. 509-526.
He, X. 2000, 'Stability And Delays In A Predator-prey System - Ii', Dynamics Of Continuous Discrete And Impulsive Systems, vol. 7, no. 2, pp. 177-187.
As a continuation of author's recent work (J. Math. Anal. Appl., 198 (1996), 355-370), a classical autonomous Lotka-Volterra predator-prey model with variable bounded delays is concerned. By means of Lyapunov functionals, we establish sufficient conditio
Li, J., Liu, Z. & He, X. 1999, 'Periodic Solutions Of Some Differential Delay Equations Created By Hamiltonian Systems', Bulletin Of The Australian Mathematical Society, vol. 60, no. 3, pp. 377-390.
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This paper is concerned with finding periodic solutions of differential delay systems [GRAPHICS] and [GRAPHICS] where r(i) (i = 1, 2,... n - 1) are positive constants. By using the theory of Hamiltonian systems, we obtain some sufficient conditions under
Li, J. & He, X. 1999, 'Proof And Generalization Of Kaplan-yorke's Conjecture Under The Condition F ' (0) > 0 On Periodic Solution Of Differential Delay Equations', Science In China Series A-mathematics Physics Astronomy, vol. 42, no. 9, pp. 957-964.
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Using the theory of existence of periodic solutions of Hamiltonian systems, it is shown that many periodic solutions of differential delay equations can be yielded from many families of periodic solutions of the coupled generalized Hamiltonian systems. S
He, X. 1999, 'Degenerate Lyapunov Functionals Of A Well-known Prey-predator Model With Discrete Delays', Proceedings Of The Royal Society Of Edinburgh Section A-mathematics, vol. 129, pp. 755-771.
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It is commonly believed that, as far as stabilities are concerned, small delays are negligible in some modelling processes. However, to have an affirmative answer for this common belief is still an open problem for many nonlinear equations. In this paper
Li, J., He, X. & Liu, Z. 1999, 'Hamiltonian Symmetric Groups And Multiple Periodic Solutions Of Differential Delay Equations', Nonlinear Analysis-theory Methods & Applications, vol. 35, no. 4, pp. 457-474.
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He, X. 1998, 'The Lyapunov Functionals For Delay Lotka-volterra-type Models', Siam Journal On Applied Mathematics, vol. 58, no. 4, pp. 1222-1236.
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By means of Lyapunov functionals, we have succeeded in establishing the global attractivity of the positive equilibrium of n-species Lotka-Volterra systems modeled by equations of the pure-delay type with both finite and infinite delays involved. As a co
He, X. 1998, 'Almost Periodic Solutions Of A Competition System With Dominated Infinite Delays', Tohoku Mathematical Journal, vol. 50, no. 1, pp. 71-89.
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In this paper, we consider an n-species almost periodic Lotka-Volterra competition system with dominated infinite delays. By constructing suitable Lyapunov functionals, we are able to show that, under a set of algebraic conditions, the system has a uniqu
He, X., Xia, H. & Ruan, D. 1998, 'Global Stability In Chemostat-type Equations With Distributed Delays', Siam Journal On Mathematical Analysis, vol. 29, no. 3, pp. 681-696.
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We consider a chemostat-type model in which a single species feeds on a limiting nutrient supplied at a constant rate. The model incorporates a general nutrient uptake function and two distributed (infinite) delays. The first delay models the fact that t
Li, J. & He, X. 1998, 'Multiple Periodic Solutions Of Differential Delay Equations Created By Asymptotically Linear Hamiltonian Systems', Nonlinear Analysis-theory Methods & Applications, vol. 31, no. 1-2, pp. 45-54.
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He, X. & Ruan, D. 1998, 'Global Stability In Chemostat-type Plankton Models With Delayed Nutrient Recycling', Journal Of Mathematical Biology, vol. 37, no. 3, pp. 253-271.
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In this paper, we consider chemostat-type plankton models in which plankton feeds on a limiting nutrient and the nutrient is supplied at a constant rate and is partially recycled after the death of plankton by bacterial decomposition. We use a distribute
Ruan, D. & He, X. 1998, 'Global Stability In Chemostat-type Competition Models With Nutrient Recycling', Siam Journal On Applied Mathematics, vol. 58, no. 1, pp. 170-192.
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Freedman and Xu [J. Math. Biol., 31 (1993), pp. 513-527] proposed two chemostat-type competition models with nutrient recycling. In the first model the recycling is instantaneous, whereas in the second, the recycling is delayed. They carried out the equi
He, X. & Gopalsamy, K. 1997, 'Persistence, Attractivity, And Delay In Facultative Mutualism', Journal Of Mathematical Analysis And Applications, vol. 215, no. 1, pp. 154-173.
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Relations between persistence and ultimate boundedness of the solutions of the Lotka-Volterra system dx(t)/dt = x(t)[r(1) - a(11)x(t - tau) + a(22)y(t - tau)] dy(t)/dt = y(t)[r(2) + a(21)x(t - tau) - a(22)y(t - tau)] modelling ''facultative mutualism'' w
Gopalsamy, K. & He, X. 1997, 'Oscillations And Convergence In An Almost Periodic Competition System', Acta Applicandae Mathematicae, vol. 46, no. 3, pp. 247-266.
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Sufficient conditions are derived for the existence of a globally attractive almost periodic solution of a competition system modelled by the nonautonomous Lotka-Volterra delay differential equations dN(1)(t)/dt = N-1(t)[r(1)(t) - a(11)(t)N-1(t-r(t)) - a
He, X. 1996, 'Stability And Delays In A Predator-prey System', Journal Of Mathematical Analysis And Applications, vol. 198, no. 2, pp. 355-370.
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Sufficient conditions for both local and global stability of the positive equilibrium in a predator-prey system with time delays are obtained by constructing suitable Lyapunov functionals. A remark on the mistake by K. N. Murty and M. A. S. Srinivas (J.
Gopalsamy, K., He, X. & Sun, D. 1995, 'On The Oscillatory Convergence Of Solutions Of A Neutral Delay Diffusion Equation', International Journal Of Systems Science, vol. 26, no. 3, pp. 563-576.
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Sufficient conditions are obtained for the trivial solution of the initial-boundary value problem partial derivative/partial derivative t [u(t, X) - cu(t - sigma, x)] = D partial derivative(2)u(t, x)/partial derivative x(2) - au(t - tau, x) partial deriv
He, X., Zhang, B. & Gopalsamy, K. 1994, 'Single-species Dynamics In Changing Environments', Dynamics And Stability Of Systems, vol. 9, no. 4, pp. 293-303.
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A priori bounds are obtained for positive solutions of scalar delay differential equations of the form dN(t)/dt=N(t)f(t,N(t-tau(t)) modelling single species dynamics in a temporally changing environment. Sufficient conditions are derived for the existenc
Gopalsamy, K. & He, X. 1994, 'Delay-independent Stability In Bidirectional Associative Memory Networks', Ieee Transactions On Neural Networks, vol. 5, no. 6, pp. 998-1002.
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It is shown that if the neuronal gains are small compared with the synaptic connection weights, then a bidirectional associative memory network with axonal signal transmission delays converges to the equilibria associated with exogenous inputs to the net
He, X. & Gopalsamy, K. 1994, 'Persistence, Stability And Level-crossings In An Integrodifferential System', Journal Of Mathematical Biology, vol. 32, no. 5, pp. 395-426.
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Dynamical characteristics of an integrodifferential system modelling two species competition with hereditary effects are investigated; in particular we derive sufficient conditions for the persistence of the species, existence of an attracting periodic s
Gopalsamy, K. & He, X. 1994, 'Stability In Asymmetric Hopfield Nets With Transmission Delays', Physica D, vol. 76, no. 4, pp. 344-358.
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Sufficient conditions are derived for the delay independent stability of the equilibria in Hopfield's graded response networks of the type dx(i)(t)/dt = -b(i)x(i)(t) + SIGMA(j=1)n a(ij)f(j)(mu(j)x(j)(t - tau(ij)) + F(i)(t) (i = 1,2,...,n) when the extern
Gopalsamy, K., He, X. & Sun, D. 1993, 'Oscillations And Convergence In A Diffusive Delay Logistic Equation', Mathematische Nachrichten, vol. 164, pp. 219-237.
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Sufficient conditions are obtained for all positive solutions of the diffusive delay-logistic system partial derivative N(x, t)/partial derivative t = D partial derivative 2N(x, t)/partial derivative x2 + rN(x, t)[1- N(x, t - tau/K] partial derivative N/
Gopalsamy, K., Wen, L., Chen, Y. & He, X. 1993, 'Necessary And Sufficient Conditions For A 4th-order Functional-differential Equation To Be Oscillatory', Mathematische Nachrichten, vol. 164, pp. 23-36.
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Necessary and sufficient conditions for a fourth order functional differential equation of the form (1) [r(t) y (t)] + f(t, y(h1(t)), y(h2(t)), ..., y(h(n)(t))) = 0 to be oscillatory are given when.f is strongly superlinear or strongly sublinear.
Gopalsamy, K., He, X. & Wen, L. 1991, 'Global Attractivity And Oscillations In A Periodic Logistic Integrodifferential Equation', Houston Journal Of Mathematics, vol. 17, no. 2, pp. 157-177.
Sufficient conditions are obtained for the existence of a globally attracting periodic solution of the logistic integrodifferential equation [GRAPHICS] We also derive sufficient conditions for all positive solutions of (*) to oscillate about the unique p
Gopalsamy, K., He, X. & Wen, L. 1991, 'On A Periodic Neutral Logistic Equation', Glasgow Mathematical Journal, vol. 33, pp. 281-286.
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He, X. & Shi, L. 2010, 'Differences in opinion and risk premium', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 271 Abstract: When people agree to disagree, this paper examines the impact of the disagreement among agents on market equilibrium and equity premium. Within the standard mean variance framework, we consider a market of two risky assets, a riskless asset and two (and then a continuum of) agents who have different preferences and heterogeneous beliefs in the means and variance/covariances of the asset returns. By constructing a consensus belief, we introduce a boundedly rational equilibrium (BRE) to characterize the market equilibrium and derive a CAPM under heterogeneous beliefs. When the differences in opinion are formed as mean-preserving spreads of a benchmark homogeneous belief, we analyz eexplicitly the impact on the market equilibrium and risk premium, showing that the risk tolerance, optimism/pessimism and con?dence/doubt can jointly generate high risk premium and low risk-free rate.
He, X. & Zheng, M. 2010, 'Dynamics of moving average rules in a continuous-time financial market model', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 268 Abstract: Within a continuous-time framework, this paper proposes a stochastic heterogeneous agent model (HAM) of financial markets with time delays to unify various moving average rules used indiscrete-time HAMs. The time delay represents a memory length of a moving average rule indiscrete-time HAMs.Intuitive conditions for the stability of the fundamental price of the deterministic model in terms of agents' behavior parameters and memory length are obtained. It is found that an increase in memory length not only can destabilize the market price, resulting in oscillatory market price characterized by a Hopf bifurcation, but also can stabilize another wise unstable market price, leading to stability switching as the memory length increases. Numerical simulations show that the stochastic model is able to characterize long deviations of the market price from its fundamental price and excess volatility and generate most of the stylized factso bserved in financial markets.
Chiarella, C., He, X. & Zheng, M. 2009, 'Heterogeneous Expectations and Exchange Rate Dynamics (243)', Quantitative Finance Research Paper Series.
This paper presents a continuous-time model of exchange rates relying not only on macroeconomic factors but also having a market microstructure component. The driving macroeconomic factor is the interest rate differential, while the market microstructure element is described by the expectations of boundedly rational portfolio managers who use a weighted average of the expectations of fundamentalists and chartists. Within this framework, the different roles of the macroeconomic factors and market microstructure elements on the determination of the exchange rate are examined explicitly. We show that this simple model generates very complicated market behaviour, including the existence of multiple steady state equilibria, the deviations of the market exchange rate from the fundamental, and market fluctuations. Numerical simulation of the corresponding stochastic version of the model shows that the model is able to generate typical time series and volatility clustering patterns observed in exchange rate markets.
He, X., Li, K., Wei, J. & Zheng, M. 2009, 'Market stability switches in a continuous-time financial market with heterogeneous beliefs', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 252 Abstract: By considering a financial market of fundamentalists and trend followers in which the price trend of the trend followers is formed as a weighted average of historical prices, we establish a continuous-time financial market model with time delay and examines the impact of time delay on market price dynamics. Conditions for the stability of the fundamental price in terms of agents' behavior parameters and time delay are obtained. In particular, it is found that an increase in time delay can not only destabilize the market price but also stabilize an otherwise unstable market price, leading to stability switching as delay increases. This interesting phenomena shed new light in understanding of mechanism on the market stability. When the fundamental price becomes unstable through Hopf bifurcations, suffcient conditions on the stability and global existence of the periodic solution are obtained.
He, X. & Shi, L. 2009, 'Portfolio analysis and zero-beta CAPM with heterogeneous beliefs', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 244 Abstract: With the standard mean variance framework, by assuming heterogeneity and bounded rationality of investors, this paper examines their impact on the market equilibrium and implications to the portfolio analysis. By constructing a market consensus belief, we establish market equilibrium prices of risky assets and show that the standard Blacks zero-beta CAPM under homogeneous beliefs holds under the heterogeneous belief. We demonstrate that the biased belief (from the market consensus belief) of investors makes their optimal portfolio not necessarily locate on the market mean-variance frontier. We show that the traditional geometric relation of the mean variance frontiers with and without the riskless asset under the homogeneous beliefs does not hold under the heterogeneous beliefs. The results shed light on the risk premium puzzle, Millers hypothesis, the lower market performance when the access to the risk free asset is impossible, and the empirical finding that managed funds under-perform comparing to the market indices on average.
Chiarella, C., Dieci, R. & He, X. 2009, 'A framework for CAPM with heterogenous beliefs', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 254 Abstract: We introduce heterogeneous beliefs in to the mean-variance framework of the standard CAPM, in contrast to the standard approach which assumes homogeneous beliefs. By assuming that agents form optimal portfolios based upon their heterogeneous beliefs about conditional means and covariances of the risky asset returns, we set up a framework for the CAPM that incorporates the heterogeneous beliefs when the market is in equilibrium. In this framework we first construct a consensus belief (with respect to the means and covariances of the risky asset returns) to represent the aggregate market belief when the market is in equilibrium. We then extend the analysis to a repeated one-period set-up and establish a framework for a dynamic CAPM using a market fraction model in which agents are grouped according to their beliefs. The exact relation between heterogeneous beliefs, the market equilibrium returns and the ex-ante beta-coeffcients is obtained. CAPM and Heterogeneous beliefs.
Chiarella, C., Dieci, R. & He, X. 2008, 'Heterogeneity, Market Mechanisms, and Asset Price Dynamics', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydnet.
Research Paper Number: 231 Abstract: This chapter surveys the boundedly rational heterogeneous agent (BRHA) models of financial markets, to the development of which the authors and several co-authors have contributed in various papers. We give particular emphasis to role of the market clearing mechanism used, the utility function of the investors, the interaction of price and wealth dynamics, portfolio implications, the impact of stochastic elements on the markets dynamics, and calibration of this class of models. Due to agents behavioural features and market noise, the BRHA models are both nonlinear and stochastic. We show that the BRHA models produce both a locally stable fundamental equilibrium corresponding to that of standard paradigm, as well as instability with a consequent rich range of possible complex behaviours characterised both indirectly by simulation and directly by stochastic bifurcations. A calibrated model is able to reproduce quite well the stylized facts of financial markets. The BRHA framework is thus able to accommodate market features that seem not easily reconcilable for the standard financial market paradigm, such as fat tail, volatility clustering, large excursions from the fundamental and bubbles.
He, X. & Shi, L. 2008, 'Heterogeneity, bounded rationality and market dysfunctionality', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 233 Abstract: As the main building blocks of the modern finance theory, homogeneity and rational expectation have faced difficulty in explaining many market anomalies, stylized factors, and market inefficiency in empirical studies. As a result, heterogeneity and bounded rationality have been used as an alterative paradigm of asset price dynamics and this paradigm has been widely recognized recently in both academic and financial market practitioners. Within the framework of Chiarella, Dieci and He (2006a, 2006b) on mean-variance analysis under heterogeneous beliefs in terms of either the payoffs or returns of the risky assets, this paper examines the effect of the heterogeneity. We first demonstrate that, in market equilibrium, the standard one fund theorem under homogeneous belief does not held under heterogeneous belief in general, however, the optimal portfolios of investors are very close to the market efficient frontier. By imposing certain distribution assumption on the heterogeneous beliefs, we then use Monte Carlo simulations to show that certain heterogeneity among investors can improve the Sharpe and Treynor ratios of the portfolios and investors can benefit from the diversity in investors beliefs. We also show that non-normality of market equilibrium return distributions is an outcome of the market aggregation of individual investors who make rational decisions based on their beliefs. Our results explain the empirical funding that that managed funds under-perform the market index on average and show that heterogeneity can improve the market efficiency.
Chiarella, C., He, X. & Zheng, M. 2007, 'The Stochastic Dynamics of Speculative Prices (208)', Quantitative Finance Research Paper Series.
Within the framework of the heterogeneous agent paradigm, we establish a stochastic model of speculative price dynamics involving of two types of agents, fundamentalists and chartists, and the market price equilibria of which can be characterised by the invariant measures of a random dynamical system. By conducting a stochastic bifurcation analysis, we examine the market impact of speculative behaviour. We show that, when the chartists use lagged price trends to form their expectations, the market equilibrium price can be characterised by a unique and stable invariant measure when the activity of the speculators is below a certain critical value. If this threshold is surpassed, the market equilibrium can be characterised by more than two invariant measures, of which one is completely stable, another is completely unstable and the remaining ones may exhibit various types of stability. Also, the corresponding stationary measure displays a significant qualitative change near the threshold value. We show that the stochastic model displays behaviour consistent with that of the underlying deterministic model. However, when the time lag in the formation of the price trends used by the chartists approaches zero, such consistency breaks down. In addition, the change in the stationary distribution is consistent with a number of market anomalies and stylised facts observed in financial markets, including a bimodal logarithmic price distribution and fat tails.
Gao, J., Gong, G. & He, X. 2007, 'Monetary policy and exchange rate regime: Proposal for a small and less developed economy', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 199 Abstract: We investigate monetary policy under the assumption that a countrys capital market is open? under the WTO framework while the exchange rate is fixed. Our purpose is to determine if it is possible in this case for the economy to maintain an effective monetary policy for stabilizing the domestic economy. For this, we suggest two institutional restrictions. Given the restrictions, we demonstrate within a macro-dynamic model that monetary policy can still be effective. The implication of such an institutional design for an exchange rate regime is also discussed with special reference to small and less development economies.
Chiarella, C. & He, X. 2006, 'Aggregation of heterogeneous beliefs and asset pricing theory: A mean-variance analysis', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Paper Number: 186
Corron, N., He, X. & Westerhoff, F.H. 2005, 'Butter mountains, milk lakes and optimal price limiters (QFRC paper #158)'.
ISSN 1441-8010 www.business.uts.edu.au/qfrc/research/research_papers/rp158.pdf
Dieci, R., Foroni, I., Gardini, L. & He, X. 2005, 'Market mood, adaptive beliefs and asset price dynamics (QFRC paper #162)'.
ISSN 1441-8010 www.business.uts.edu.au/qfrc/research/research_papers/rp162.pdf
He, X. & Li, Y. 2005, 'Long memory, heterogeneity and trend chasing (QFRC paper #148)'.
ISSN 1441-8010 www.business.uts.edu.au/qfrc/research/research_papers/rp148.pdf
He, X. & Li, Y. 2005, 'Heterogeneity, profitability and autocorrelations (QFRC paper #147)'.
ISSN 1441-8010 www.business.uts.edu.au/qfrc/research/research_papers/rp147.pdf
Chiarella, C., He, X. & Hommes, C. 2004, 'A dynamic analysis of moving average rules (QFRC paper #133)'.
He, X. & Westerhoff, F.H. 2004, 'Commodity markets, price limiters and speculative price dynamics (QFRC paper #136)'.
Chiarella, C., He, X. & Hommes, C. 2004, 'A dynamic analysis of moving average rules (Centre for Nonlinear Dynamics in Economics & Finance, University of Amsterdam, paper #04-14)', 10th International conference on computing in economics and finance.
Chiarella, C., He, X. & Wang, D. 2004, 'Statistical Properties of a Heterogeneous Asset Price Model with Time-Varying Second Moment', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 142 Abstract: Stability and bifurcation analysis of deterministic systems has been widely used in modeling financial markets. However, the impact of such dynamic phenomena on various statistical properties of the corresponding stochastic model, including skewness and excess kurtosis, various autocorrelation (AC) patterns of under and over reactions, and volatility clustering characterised by the long-range dependence of ACs, is not clear and has been very little studied. This paper aims to study this issue. Through a simple behavioural asset pricing model with fundamentalists and chartists, we examine the statistical properties of the model and their connection to the dynamics of the underlying deterministic model. In particular, our analysis leads to some insights into the type of mechanism that may be generating some of the stylised facts, such as fat tails, skewness, high kurtosis and long memory, observed in high frequency financial data.
Chiarella, C., He, X. & Wang, D. 2004, 'A behavioural asset pricing model with a time-varying second moment', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 141 Abstract: We develop a simple behavioural asset pricing model with fundamentalists and chartists to study price behaviour in financial markets. Within our model, the market impact of the weighting process of the conditional mean and variance of the chartists and investors' reactions are analysed. Price dynamics of the deterministic model under/over-reactions are analyzed. It shows different price dynamics and routes to complicated price behaviour when the chartists act as either trend followers or contrarians. It is found that (in a separate paper Chiarella et al (2004)) this analysis can be used to establish some connections between the statistical properties of the nonlinear stochastic system (such as distribution density and autocorrelation patterns of returns, in particular the stylised facts, such as fat tails, skewness, high kurtosis and long memory, observed in high frequency financial data) and the stability and bifurcation of the underlying deterministic system are established.
Chiarella, C., He, X. & Zhu, P. 2003, 'Fading memory learning in the cobweb model with risk averse heterogeneous producers (QFRC paper #108)'.
He, X. 2003, 'Asset pricing volatility and market behaviour: a market fraction approach (QFRC paper #95)'.
Chiarella, C. & He, X. 2002, 'An adaptive model on asset pricing and wealth dynamics with heterogeneous trading strategies', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 84 Abstract: This paper develops an adaptive model on asset pricing and wealth dynamic of a financial market with heterogeneous agents and examines the profitability of momentum and contrarian trading strategies. In order to characterize asset price, wealth dynamics and rational adaptiveness arising from the interaction of heterogeneous agents with CRRA utility, an adaptive discrete time equilibrium model in terms of return ad wealth proportions (among heterogeneous representative agents) is established. Taking trend followers and contrarians as the main hetergeneous agents in the model, the profitability of momentum and contrarian trading strategies is analyzed. Our results show the capability of the model to characterize some of the existing evidence on many of anomailies observed in financial markets, including the profitability of momentum trading strategies over short time intervals, rational adaptiveness of agents, overconfidence and underreaction, overreaction and herd behavior, excess volatility, and volatility clustering.
Chiarella, C. & He, X. 2001, 'Asset price and wealth dynamics under heterogeneous expectations', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 56 Abstract: In order to characterize asset price and wealth dynamics arising from the interaction of heterogeneous agents with CRRA utility, a discrete time stationary model in terms of return and wealth proportions (among different types of agents) is established. When fundamentalists and chartists are the main heterogeneous agents in the model, it is found that in the presence of heterogeneous agents the stationary model can have multiple steady-states. The steady-state is unstable when the chartists extrapolate strongly and (locally) stable when they extrapolate weakly. The convergence to steady-state follows an optimal selection principle - the return and wealth proportions tend to the steady-state which has relatively higher return. More importantly, heterogeneity can generate instability which, under the stochastic processes of the dividend yield and extrapolation rates, results in switching of the return among different states, such as steady-state, periodic and aperiodic cycles from time to time. To model that is finally developed displays the essential characteristics of the standard asset price dynamics model assumed in continuous time finance, in that the asset price is fluctuating around a geometrically growing trend. The model also displays the volatility clustering that is an essential feature of empirically observed assets returns.
Chiarella, C. & He, X. 2001, 'Dynamics of beliefs and learning under aL processes - The heterogeneous case', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 55 Abstract: This paper studies a class of models in which agents' expectations influence the actual dynamics while the expectations themselves are the outcome of some recursive processes with bounded memory. Under the assumptions of heterogeneous expectations (or beliefs) and that the agents update their expectations by recursive L- and general aL-processes, the dynamics of the resulting expectations and learning schemes are analyzed. It is shown that the dynamics of the system, including stability, instability and bifurcation, are affected differently by the recursive processes. The cobweb model with a simple heterogeneous expectation scheme is employed as an example to illustrate the stability results, the various types of bifurcations and the routes to complicated price dynamics. In particular, the double edged effect of heterogeneity on the dynamics of the model is demonstrated.
Chiarella, C. & He, X. 2001, 'Dynamics of beliefs and learning under aL processes - The homogeneous case', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 53 Abstract: This paper studies a class of models in which agents' expectations influence the actual dynamics while the expectations themselves are the outcome of some learning process. Under the assumptions that agents have homogeneous expectations (or beliefs) and that they update their expectations by least-squares L- and general aL - processes, the dynamic of the resulting expectations and learning schemes are analyzed. It is shown how the dynamics of the system, including stability, instability and bifurcation, are affected by the learning processes. The cobweb model with a simple homogeneous expectation scheme is employed as an example to illustrate the stability results, the various types of bifurcations and the routes to complicated price dynamics.
Chiarella, C. & He, X. 2000, 'Stability of competitive equilibria with heterogeneous beliefs and learning', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 37 Abstract: The paper studies a class of models in which agents' expectations influence the actual dynamics while the expectations themselves are the outcome of some learning processes. Situations of both homogeneous and heterogeneous beliefs are considered. In both cases agents update their expectations by general ah - and least-squares h-processes and the stability of the resulting dynamics in both cases is analysed. It is shown how the stability of the actual dynamics is affected by the heterogeneous expectations and different least-squares h-processes.
Chiarella, C. & He, X. 2000, 'Heterogeneous beliefs, risk and learning in a simple asset pricing model with a market maker', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 35