Asset price and wealth dynamics in a financial market with heterogeneous agents |
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| Institution: | 1. School of Finance and Economics, University of Technology Sydney P.O. Box 123 Broadway NSW 2007, Australia;2. Dipartimento di Matematica per le Scienze Economiche e Sociali, University of Bologna, I-40126 Bologna, Italy;3. Istituto di Scienze Economiche, University of Urbino, I-61029 Urbino, Italy;1. St. Louis, MO, USA;2. Amsterdam, The Netherlands;3. Amsterdam, The Netherlands;1. Department of Economics and Management, University of Pavia, Italy;2. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv School of Economics, Ukraine;3. University of Urbino Carlo Bo, Urbino, Italy;4. IST, University of Stuttgart, Stuttgart, Germany;1. School of Economics and Commerce, Guangdong University of Technology, Guangzhou 510520, China;2. School of Science, Hebei University of Technology, Tianjin 300401, China;3. Department of Mathematics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China;4. Department of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050005, China;1. College of Management and Economics, Tianjin University, Tianjin 300072, China;2. China Center for Social Computing and Analytics, Tianjin University, Tianjin 300072, China;3. CNRS, Center d’Economie de la Sorbonne, Université Paris 1 Panthéon-Sorbonne, 106-112 Boulevard de l’Hôpital 75647 Paris Cedex 13, France |
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| Abstract: | This paper considers a discrete-time model of a financial market with one risky asset and one risk-free asset, where the asset price and wealth dynamics are determined by the interaction of two groups of agents, fundamentalists and chartists. In each period each group allocates its wealth between the risky asset and the safe asset according to myopic expected utility maximization, but the two groups have heterogeneous beliefs about the price change over the next period: the chartists are trend extrapolators, while the fundamentalists expect that the price will return to the fundamental. We assume that investors’ optimal demand for the risky asset depends on wealth, as a result of CRRA utility. A market maker is assumed to adjust the market price at the end of each trading period, based on excess demand and on changes of the underlying reference price. The model results in a nonlinear discrete-time dynamical system, with growing price and wealth processes, but it is reduced to a stationary system in terms of asset returns and wealth shares of the two groups. It is shown that the long-run market dynamics are highly dependent on the parameters which characterize agents’ behaviour as well as on the initial condition. Moreover, for wide ranges of the parameters a (locally) stable fundamental steady state coexists with a stable ‘non-fundamental’ steady state, or with a stable closed orbit, where only chartists survive in the long run: such cases require the numerical and graphical investigation of the basins of attraction. Other dynamic scenarios include periodic orbits and more complex attractors, where in general both types of agents survive in the long run, with time-varying wealth fractions. |
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