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Limit Distribution of Evolving Strategies in Financial Markets

In this paper we model a financial market composed of agents with heterogeneous beliefs who change their strategy over time. We propose two different solution methods which lead to two different types of endogenous dynamics. The first makes use of the maximum entropy approach to obtain an exponential type probability function for strategies, analogous to the well known Brock and Hommes (1997) model, but with the endogenous specification for the intensity of choice parameter, which varies over time as a consequence of the relative performances of each strategy. The second type of dynamics is obtained by setting up a master equation and solving it using recently developed asymptotic solution techniques, which yield a system of differential equations describing the evolution of the share of each strategy in the market. The performance sof the two solutions are then compared and contrasted with the empirical evidence.

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File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp294.pdf
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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 294.

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Length: 28
Date of creation: 01 Aug 2011
Date of revision:
Handle: RePEc:uts:rpaper:294
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  1. Clementi, F. & Di Matteo, T. & Gallegati, M., 2006. "The power-law tail exponent of income distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 49-53.
  2. Lux, Thomas, 1998. "The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions," Journal of Economic Behavior & Organization, Elsevier, vol. 33(2), pages 143-165, January.
  3. repec:cup:cbooks:9780521831062 is not listed on IDEAS
  4. Carl Chiarella & Tony He & Cars H. Hommes, 2005. "A Dynamic Analysis of Moving Average Rules," Tinbergen Institute Discussion Papers 05-057/1, Tinbergen Institute.
  5. Pfajfar, Damjan & Santoro, Emiliano, 2010. "Heterogeneity, learning and information stickiness in inflation expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 75(3), pages 426-444, September.
  6. Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2008. "Heterogeneity, Market Mechanisms, and Asset Price Dynamics," Research Paper Series 231, Quantitative Finance Research Centre, University of Technology, Sydney.
  7. Carl Chiarella & Xue-Zhong He, 2001. "Dynamics of Beliefs and Learning Under aL Processes - The Heterogeneous Case," Research Paper Series 55, Quantitative Finance Research Centre, University of Technology, Sydney.
  8. Beja, Avraham & Goldman, M Barry, 1980. " On the Dynamic Behavior of Prices in Disequilibrium," Journal of Finance, American Finance Association, vol. 35(2), pages 235-48, May.
  9. Simone Landini & Corrado Di Guilmi & Mauro Gallegati, 2008. "A Maxent Model For Macroscenario Analysis," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 11(05), pages 719-744.
  10. Paul De Grauwe, 2010. "Top-Down versus Bottom-Up Macroeconomics," CESifo Working Paper Series 3020, CESifo Group Munich.
  11. Day, Richard H. & Huang, Weihong, 1990. "Bulls, bears and market sheep," Journal of Economic Behavior & Organization, Elsevier, vol. 14(3), pages 299-329, December.
  12. Carl Chiarella & Corrado Di Guilmi, 2010. "The Financial Instability Hypothesis:a Stochastic Microfoundation Framework," Research Paper Series 273, Quantitative Finance Research Centre, University of Technology, Sydney.
  13. Carl Chiarella, 1992. "The Dynamics of Speculative Behaviour," Working Paper Series 13, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
  14. Lux, Thomas, 1995. "Herd Behaviour, Bubbles and Crashes," Economic Journal, Royal Economic Society, vol. 105(431), pages 881-96, July.
  15. Simone Alfarano & Thomas Lux & Friedrich Wagner, 2006. "Time-Variation of Higher Moments in a Financial Market with Heterogeneous Agents: An Analytical Approach," Working Papers wpn06-01, Warwick Business School, Finance Group.
  16. Paul De Grauwe, 2010. "Top-Down versus Bottom-Up Macroeconomics," CESifo Economic Studies, CESifo, vol. 56(4), pages 465-497, December.
  17. repec:cup:cbooks:9780521606196 is not listed on IDEAS
  18. Zeeman, E. C., 1974. "On the unstable behaviour of stock exchanges," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 39-49, March.
  19. Prof John Foster, 2004. "Why is Economics not a Complex Systems Science?," Discussion Papers Series 336, School of Economics, University of Queensland, Australia.
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