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Non-ergodic Behavior in a Financial Market with Interacting Investors

Author

Listed:
  • Ulrich Horst

    (University of British Columbia)

  • Jan Wezelburger

Abstract

We identify possible long-run market shares and the long-run asset price dynamics of financial markets with heterogenous interacting agents. This involves stability conditions for a class of difference equation in a random environment, where the random environment is endogenously generated by agents' investment behavior. Depending on the evaluation of a performance measure of an investment, asset prices may behave in a non-ergodic manner. That is, the price processes converge in distribution, but the limiting distribution is not necessarily uniquely determined. The long-run market shares of two competing financial mediators may strongly depend on the random environment which is endogenously generated by a noise traders

Suggested Citation

  • Ulrich Horst & Jan Wezelburger, 2006. "Non-ergodic Behavior in a Financial Market with Interacting Investors," 2006 Meeting Papers 229, Society for Economic Dynamics.
    • Handle: RePEc:red:sed006:229
    as

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    References listed on IDEAS

    as
    1. repec:bla:jfinan:v:44:y:1989:i:3:p:681-96 is not listed on IDEAS
    2. Bohm, Volker & Wenzelburger, Jan, 2005. "On the performance of efficient portfolios," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 721-740, April.
    3. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    4. J. Bradford De Long & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann, 1989. "The Size and Incidence of the Losses from Noise Trading," Journal of Finance, American Finance Association, vol. 44(3), pages 681-696, July.
    5. Igor Evstigneev & Thorsten Hens & Klaus Schenk-Hoppé, 2006. "Evolutionary stable stock markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(2), pages 449-468, January.
    6. De Long, J Bradford & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann, 1990. "Noise Trader Risk in Financial Markets," Journal of Political Economy, University of Chicago Press, vol. 98(4), pages 703-738, August.
    7. Marten Hillebrand, 2004. "The Impact of Multiperiod Planning Horizons on Portfolios and Asset Prices," Computing in Economics and Finance 2004 259, Society for Computational Economics.
    8. Hens, Thorsten & Schenk-Hoppe, Klaus Reiner, 2005. "Evolutionary stability of portfolio rules in incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 43-66, February.
    9. William A. Brock & Steven N. Durlauf, 2002. "A Multinomial-Choice Model of Neighborhood Effects," American Economic Review, American Economic Association, vol. 92(2), pages 298-303, May.
    10. Alvaro Sandroni, 2000. "Do Markets Favor Agents Able to Make Accurate Predicitions?," Econometrica, Econometric Society, vol. 68(6), pages 1303-1342, November.
    11. De Long, J Bradford & Shleifer, Andrei & Summers, Lawrence H & Waldmann, Robert J, 1991. "The Survival of Noise Traders in Financial Markets," The Journal of Business, University of Chicago Press, vol. 64(1), pages 1-19, January.
    12. William A. Brock & Steven N. Durlauf, 2001. "Discrete Choice with Social Interactions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(2), pages 235-260.
    13. Bisin, Alberto & Verdier, Thierry, 2001. "The Economics of Cultural Transmission and the Dynamics of Preferences," Journal of Economic Theory, Elsevier, vol. 97(2), pages 298-319, April.
    14. Volker Böhm & Nicole Deutscher & Jan Wenzelburger, 2000. "Endogenous Random Asset Prices in Overlapping Generations Economies," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 23-38, January.
    15. Andrew W. Lo & Harry Mamaysky & Jiang Wang, 2000. "Foundations of Technical Analysis: Computational Algorithms, Statistical Inference, and Empirical Implementation," Journal of Finance, American Finance Association, vol. 55(4), pages 1705-1765, August.
    16. Ulrich Horst, 2005. "Financial price fluctuations in a stock market model with many interacting agents," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(4), pages 917-932, June.
    17. Sims, Christopher A., 2003. "Implications of rational inattention," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 665-690, April.
    18. Hillebrand, Marten & Wenzelburger, Jan, 2006. "The impact of multiperiod planning horizons on portfolios and asset prices in a dynamic CAPM," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 565-593, August.
    19. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
    20. Brock, William & Lakonishok, Josef & LeBaron, Blake, 1992. "Simple Technical Trading Rules and the Stochastic Properties of Stock Returns," Journal of Finance, American Finance Association, vol. 47(5), pages 1731-1764, December.
    21. repec:bla:jfinan:v:55:y:2000:i:4:p:1705-1770 is not listed on IDEAS
    22. Armen A. Alchian, 1950. "Uncertainty, Evolution, and Economic Theory," Journal of Political Economy, University of Chicago Press, vol. 58(3), pages 211-211.
    23. Jeffrey A. Frankel & Kenneth A. Froot, 1986. "The Dollar as Speculative Bubble: A Tale of Fundamentalists and Chartists," NBER Working Papers 1854, National Bureau of Economic Research, Inc.
    24. Kuan, Chung-Ming & White, Halbert, 1994. "Adaptive Learning with Nonlinear Dynamics Driven by Dependent Processes," Econometrica, Econometric Society, vol. 62(5), pages 1087-1114, September.
    25. Chen, Xiaohong & White, Halbert, 1998. "Nonparametric Adaptive Learning with Feedback," Journal of Economic Theory, Elsevier, vol. 82(1), pages 190-222, September.
    26. LeBaron, Blake & Arthur, W. Brian & Palmer, Richard, 1999. "Time series properties of an artificial stock market," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1487-1516, September.
    27. Volker Böhm & Carl Chiarella, 2005. "Mean Variance Preferences, Expectations Formation, And The Dynamics Of Random Asset Prices," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 61-97, January.
    28. Alan P. Kirman, 1992. "Whom or What Does the Representative Individual Represent?," Journal of Economic Perspectives, American Economic Association, vol. 6(2), pages 117-136, Spring.
    29. Hans Föllmer & Martin Schweizer, 1993. "A Microeconomic Approach to Diffusion Models For Stock Prices," Mathematical Finance, Wiley Blackwell, vol. 3(1), pages 1-23, January.
    30. Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, vol. 58(1), pages 9-40, October.
    31. Gao, Fu-Qing, 1996. "Moderate deviations for martingales and mixing random processes," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 263-275, February.
    32. Follmer, Hans & Horst, Ulrich & Kirman, Alan, 2005. "Equilibria in financial markets with heterogeneous agents: a probabilistic perspective," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 123-155, February.
    33. Wenzelburger, Jan, 2004. "Learning to predict rationally when beliefs are heterogeneous," Journal of Economic Dynamics and Control, Elsevier, vol. 28(10), pages 2075-2104, September.
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    More about this item

    Keywords

    financial markets; interaction; random difference equations; stochastic approximation;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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