The Evolution Dynamic and Long-Run Equilibrium in a Stock Market with Heterogeneous Traders

Abstract

This paper uses ideas from biological evolution to analyze the evolution of the securities market in which rational and irrational traders coexist. A market evolutionary model is developed to describe the dynamic trajectories of rational and irrational traders’ wealth. The main question is, are irrational traders eliminated as the securities market evolves. The paper considers the impact of new entrants on the security market long-term equilibrium. In addition, it discusses the existence and uniqueness of the long-term equilibrium The paper finds that, under some market conditions, irrational traders could survive in the long run.

Keywords

Behavioral Finance / irrational traders / financial evolution theory / random dynamic system

References

[1] Akbas F, Armstrong W J, Sorescu S, Subrahmanyam A. Smart money, dumb money, and capital market anomalies. Journal of Finance Economics, 2015, 118(2): 355-382.

[2] Alchian A A. Uncertainty, evolution, and economic theory. The Journal of Political Economics, 1951, 58(3): 211-221.

[3] Biais B, Shadur R. Darwinian selection does not eliminate irrational traders. European Economic Review, 2000, 44(3): 469-490.

[4] Blume L, Easley D. Evolution and market behavior. Journal of Economic Theory, 1992, 58: 9-40.

[5] Blume L, Easley D. If you’re so smart, why aren’t you rich? Belief selection in complete and incomplete markets. Econometrica, 2006, 74(4): 929-966.

[6] Bottazzi G, Dindo P. Evolution and market behavior with endogenous investment rules. Journal of Economic Dynamics and Control, 2014 121-146.

[7] Bottazzi G, Giachini D. Wealth and price distribution by diffusive approximation in a repeated prediction market. Physica A: Statistical Mechanics and Its Applications, 2017, 471: 473-479.

[8] Bottazzi G, Dindo P, Giachini D. Long-run heterogeneity in an exchange economy with fixed-mix traders. Economic Theory, 2017, 66(2): 407-447.

[9] Chiarella C, Dieci R G L. Asset price and wealth dynamics in a financial market with heterogeneous agents. Journal of Economic Dynamics and Control, 2006 1755-1786.

[10] Evstigneev IV, Hens T, Schenk-Hoppe KR. Evolutionary stable stock markets. Journal of Economic Theory, 2006, 27(6): 449-468.

[11] Fama EF. The behavior of stock-market prices. Journal of Business, 1965, 38(1): 34-105.

[12] Fama EF. Efficient capital markets: A review of theory and empiricalwork. Journal of Finance, 1970, 25(3): 383-417.

[13] Fama EF. Efficient capital markets: II. Journal of Finance, 1991, 36(11): 1575-1617.

[14] Friedman M. The case for flexible exchange rates. Essays in Positive Economics, 1953, Chicago: University of Chicago Press

[15] Grinblatt M, Titman S. Performance measurement without benchmarks: An examination of mutual fund returns. The Journal of Business66, 1993

[16] Guo J, He XD. Equilibrium asset pricing with Epstein-Zin and loss-averse investors. Journal of Economic Dynamics and Control, 2017, 76: 86-108.

[17] Hirshleifer D, Subrahmanyamb A, Titman S. Feedback and the success of irrational investors. Journal of Financial Economics, 2005, 32(5): 1-28.

[18] Higham DJ. Mean-square and asymptotic stability of the stochastic theta method. Siam Journal on Numerical Analysis, 2000, 38(3): 753-769.

[19] Ikeda N, Watanabe S. A comparison theorem for solutions of stochastic differential equations and its applications. Osaka Journal of Math, 1977, 14(3): 619-633.

[20] Kahneman D, Tversky A. Loss aversion in riskless choice: A reference-dependent model. The Quarterly Journal of Economics, 1991, 106(4): 1039-1061.

[21] Lin L, Sornette D. Diagnostics of rational expectation financial bubbles with stochastic mean-reverting termination times. European Journal of Finance, 2013, 19(5): 344-365.

[22] Lo AW. The three P’s of total risk management. Financial Analysts Journal, 1999, 55(1): 13-26.

[23] Lo AW. The adaptive market hypothesis: markets efficiency from an evolutionary perspective. Journal of Portfolio Management, 2004, 31(1): 21-44.

[24] Oksendal B. Stochastic Differential Equations, 2003, Berlin: Springer-Verlag.

[25] Sandroni A. Market selection when markets are incomplete. Journal of Mathematical Economics, 2005, 41: 91-104.

[26] Seather BE, Engen SLR. Estimating the time to extinction in an island population of song sparrows. Proceedings of Theory Society of London. Series B, 2000, 267: 621-626.

[27] Tversky A, Kahneman D. Prospect theory: An analysis of decision under risk. Econometrica, 1979, 47(2): 263-292.

[28] Yan H. Natural selection in financial markets: Does it work?. Management Science, 2008, 54: 1935-1950.

[29] Yang Z, Qin G. Continuous time evolutionary financial model and globally asymptotically evolutionary stable strategies. Economic Research Journal, 2006, 5: 41-49.

[30] Zhang YJ, Zhang W, Xiong X. Strategies and investment returns: Agent based computational finance perspective. Journal of Management Science in China, 2010, 13(9): 109-118.