IDEAS home Printed from https://ideas.repec.org/p/uts/rpaper/294.html
   My bibliography  Save this paper

Limit Distribution of Evolving Strategies in Financial Markets

Author

Abstract

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.

Suggested Citation

  • Carl Chiarella & Corrado Di Guilmi, 2011. "Limit Distribution of Evolving Strategies in Financial Markets," Research Paper Series 294, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:294
    as

    Download full text from publisher

    File URL: https://www.uts.edu.au/sites/default/files/qfr-archive-03/QFR-rp294.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    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. Day, Richard H. & Huang, Weihong, 1990. "Bulls, bears and market sheep," Journal of Economic Behavior & Organization, Elsevier, vol. 14(3), pages 299-329, December.
    4. 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.
    5. Paul De Grauwe, 2010. "Top-Down versus Bottom-Up Macroeconomics," CESifo Economic Studies, CESifo, vol. 56(4), pages 465-497, December.
    6. William A. Brock & Cars H. Hommes, 2001. "A Rational Route to Randomness," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 16, pages 402-438, Edward Elgar Publishing.
    7. repec:hal:spmain:info:hdl:2441/f4rshpf3v1umfa09l8sao0qa3 is not listed on IDEAS
    8. Lux, Thomas, 2006. "Financial power laws: Empirical evidence, models, and mechanism," Economics Working Papers 2006-12, Christian-Albrechts-University of Kiel, Department of Economics.
    9. 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.
    10. Alfarano, Simone & Lux, Thomas & Wagner, Friedrich, 2008. "Time variation of higher moments in a financial market with heterogeneous agents: An analytical approach," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 101-136, January.
    11. Foley Duncan K., 1994. "A Statistical Equilibrium Theory of Markets," Journal of Economic Theory, Elsevier, vol. 62(2), pages 321-345, April.
    12. Chiarella, Carl & He, Xue-Zhong & Hommes, Cars, 2006. "A dynamic analysis of moving average rules," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1729-1753.
    13. Hens, Thorsten & Schenk-Hoppe, Klaus Reiner (ed.), 2009. "Handbook of Financial Markets: Dynamics and Evolution," Elsevier Monographs, Elsevier, edition 1, number 9780123742582.
    14. Leigh Tesfatsion & Kenneth L. Judd (ed.), 2006. "Handbook of Computational Economics," Handbook of Computational Economics, Elsevier, edition 1, volume 2, number 2.
    15. Sylvain Barde, 2012. "Of Ants and Voters. Maximum Entropy Prediction of Agent-Based Models with Recruitment," Revue de l'OFCE, Presses de Sciences-Po, vol. 0(5), pages 147-175.
    16. Chiarella, Carl & Di Guilmi, Corrado, 2011. "The financial instability hypothesis: A stochastic microfoundation framework," Journal of Economic Dynamics and Control, Elsevier, vol. 35(8), pages 1151-1171, August.
    17. Aoki,Masanao & Yoshikawa,Hiroshi, 2011. "Reconstructing Macroeconomics," Cambridge Books, Cambridge University Press, number 9781107634206, October.
    18. Beja, Avraham & Goldman, M Barry, 1980. "On the Dynamic Behavior of Prices in Disequilibrium," Journal of Finance, American Finance Association, vol. 35(2), pages 235-248, May.
    19. 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.
    20. Chiarella, Carl & He, Xue-Zhong, 2003. "Dynamics of beliefs and learning under aL-processes -- the heterogeneous case," Journal of Economic Dynamics and Control, Elsevier, vol. 27(3), pages 503-531, January.
    21. Sims, Christopher A., 2003. "Implications of rational inattention," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 665-690, April.
    22. Tesfatsion, Leigh & Judd, Kenneth L., 2006. "Handbook of Computational Economics, Vol. 2: Agent-Based Computational Economics," Staff General Research Papers Archive 10368, Iowa State University, Department of Economics.
    23. John Foster, 2006. "Why Is Economics Not a Complex Systems Science?," Journal of Economic Issues, Taylor & Francis Journals, vol. 40(4), pages 1069-1091, December.
    24. Friedrich Wagner, 2011. "Market clearing by maximum entropy in agent models of stock markets," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 6(2), pages 121-138, November.
    25. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    26. Aoki,Masanao, 2004. "Modeling Aggregate Behavior and Fluctuations in Economics," Cambridge Books, Cambridge University Press, number 9780521606196, October.
    27. Lux, Thomas, 1995. "Herd Behaviour, Bubbles and Crashes," Economic Journal, Royal Economic Society, vol. 105(431), pages 881-896, July.
    28. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    29. Smith, Eric & Foley, Duncan K., 2008. "Classical thermodynamics and economic general equilibrium theory," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 7-65, January.
    30. Carl Chiarella, 1992. "The Dynamics of Speculative Behaviour," Working Paper Series 13, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    31. Zeeman, E. C., 1974. "On the unstable behaviour of stock exchanges," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 39-49, March.
    32. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186, Elsevier.
    33. Alexis Toda, 2010. "Existence of a statistical equilibrium for an economy with endogenous offer sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(3), pages 379-415, December.
    34. Chiarella, Carl & He, Xue-Zhong & Hommes, Cars, 2006. "Moving average rules as a source of market instability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 12-17.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Catalano, Michele & Di Guilmi, Corrado, 2019. "Uncertainty, rationality and complexity in a multi-sectoral dynamic model: The dynamic stochastic generalized aggregation approach," Journal of Economic Behavior & Organization, Elsevier, vol. 157(C), pages 117-144.
    2. Reiner Franke & Frank Westerhoff, 2017. "Taking Stock: A Rigorous Modelling Of Animal Spirits In Macroeconomics," Journal of Economic Surveys, Wiley Blackwell, vol. 31(5), pages 1152-1182, December.
    3. Sordi, Serena & Dávila-Fernández, Marwil J., 2023. "The green-MKS system: A baseline environmental macro-dynamic model," Journal of Economic Behavior & Organization, Elsevier, vol. 212(C), pages 1056-1085.
    4. Di Guilmi, Corrado & He, Xue-Zhong & Li, Kai, 2014. "Herding, trend chasing and market volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 349-373.
    5. Kai Li, 2014. "Asset Price Dynamics with Heterogeneous Beliefs and Time Delays," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 13, July-Dece.
    6. Kai Li, 2014. "Asset Price Dynamics with Heterogeneous Beliefs and Time Delays," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2014.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2011. "The dynamic behaviour of asset prices in disequilibrium: a survey," International Journal of Behavioural Accounting and Finance, Inderscience Enterprises Ltd, vol. 2(2), pages 101-139.
    2. Kai Li, 2014. "Asset Price Dynamics with Heterogeneous Beliefs and Time Delays," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2014.
    3. Kai Li, 2014. "Asset Price Dynamics with Heterogeneous Beliefs and Time Delays," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 13, July-Dece.
    4. Agliari, Anna & Naimzada, Ahmad & Pecora, Nicolò, 2018. "Boom-bust dynamics in a stock market participation model with heterogeneous traders," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 458-468.
    5. Chiarella, Carl & He, Xue-Zhong & Zheng, Min, 2011. "An analysis of the effect of noise in a heterogeneous agent financial market model," Journal of Economic Dynamics and Control, Elsevier, vol. 35(1), pages 148-162, January.
    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. He, Xue-Zhong & Li, Youwei, 2015. "Testing of a market fraction model and power-law behaviour in the DAX 30," Journal of Empirical Finance, Elsevier, vol. 31(C), pages 1-17.
    8. Xue-Zhong He & Youwei Li, 2017. "The adaptiveness in stock markets: testing the stylized facts in the DAX 30," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 1071-1094, November.
    9. He, Xue-Zhong & Li, Youwei & Zheng, Min, 2019. "Heterogeneous agent models in financial markets: A nonlinear dynamics approach," International Review of Financial Analysis, Elsevier, vol. 62(C), pages 135-149.
    10. Di Guilmi, Corrado & He, Xue-Zhong & Li, Kai, 2014. "Herding, trend chasing and market volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 349-373.
    11. Karlis, Alexandros & Galanis, Girogos & Terovitis, Spyridon & Turner, Matthew, 2017. "Heterogeneity and Clustering of Defaults," Economic Research Papers 270011, University of Warwick - Department of Economics.
    12. Torsten Trimborn & Philipp Otte & Simon Cramer & Maximilian Beikirch & Emma Pabich & Martin Frank, 2020. "SABCEMM: A Simulator for Agent-Based Computational Economic Market Models," Computational Economics, Springer;Society for Computational Economics, vol. 55(2), pages 707-744, February.
    13. He, Xue-Zhong & Li, Kai, 2012. "Heterogeneous beliefs and adaptive behaviour in a continuous-time asset price model," Journal of Economic Dynamics and Control, Elsevier, vol. 36(7), pages 973-987.
    14. Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2013. "Time-varying beta: a boundedly rational equilibrium approach," Journal of Evolutionary Economics, Springer, vol. 23(3), pages 609-639, July.
    15. Min Zheng & Duo Wang & Xue-Zhong He, 2009. "Asymmetry of technical analysis and market price volatility," Published Paper Series 2009-6, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    16. Alessio Emanuele Biondo, 2019. "Order book modeling and financial stability," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(3), pages 469-489, September.
    17. Yu Zhang & Weihong Huang, 2018. "Impact of strategy switching on wealth accumulation," Journal of Evolutionary Economics, Springer, vol. 28(4), pages 961-983, September.
    18. Qi Nan Zhai, 2015. "Asset Pricing Under Ambiguity and Heterogeneity," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2015.
    19. Frank H. Westerhoff, 2009. "Exchange Rate Dynamics: A Nonlinear Survey," Chapters, in: J. Barkley Rosser Jr. (ed.), Handbook of Research on Complexity, chapter 11, Edward Elgar Publishing.
    20. A. K. Karlis & G. Galanis & S. Terovitis & M. S. Turner, 2021. "Heterogeneity and clustering of defaults," Quantitative Finance, Taylor & Francis Journals, vol. 21(9), pages 1533-1549, September.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:uts:rpaper:294. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Duncan Ford (email available below). General contact details of provider: https://edirc.repec.org/data/qfutsau.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.