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Price and Wealth Dynamics in a Speculative Market with an Arbitrary Number of Generic Technical Traders

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  • Mikhail Anufriev
  • Giulio Bottazzi

Abstract

We consider a simple pure exchange economy with two assets, one riskless, yielding a constant return, and one risky, paying a stochastic dividend, and we assume trading to take place in discrete time inside an endogenous price formation setting. Traders demand for the risky asset is expressed as a fraction of their individual wealth and is based on future prices forecast obtained on the basis of past market history. The general case is studied in which an arbitrary large number of heterogeneous traders operates in the market and any smooth function which maps the infinite information set to the present investment choice is allowed as agent's trading behavior. A complete characterization of equilibria is given and their stability conditions are derived. We find that this economy can only possess isolated generic equilibria where a single agent dominates the market and continuous manifolds of non-generic equilibria where many agents hold finite wealth shares. We show that irrespectively of agents number and of their behavior, all possible equilibria belong to a one dimensional "Equilibria Market Line". Finally we discuss the relative performances of different strategies and the selection principle governing market dynamics.

Suggested Citation

  • Mikhail Anufriev & Giulio Bottazzi, 2005. "Price and Wealth Dynamics in a Speculative Market with an Arbitrary Number of Generic Technical Traders," LEM Papers Series 2005/06, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    • Handle: RePEc:ssa:lemwps:2005/06
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    5. Carl Chiarella & Tony He, 2002. "An Adaptive Model on Asset Pricing and Wealth Dynamics with Heterogeneous Trading Strategies," Computing in Economics and Finance 2002 135, Society for Computational Economics.
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    8. 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.
    9. LeBaron, Blake, 2000. "Agent-based computational finance: Suggested readings and early research," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 679-702, June.
    10. Mikhail Anufriev & Giulio Bottazzi & Francesca Pancotto, 2004. "Price and Wealth Asymptotic Dynamics with CRRA Technical Trading Strategies," LEM Papers Series 2004/23, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    11. Levy, Haim & Levy, Moshe & Solomon, Sorin, 2000. "Microscopic Simulation of Financial Markets," Elsevier Monographs, Elsevier, edition 1, number 9780124458901.
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    Cited by:

    1. Hommes, C.H., 2005. "Heterogeneous Agent Models in Economics and Finance, In: Handbook of Computational Economics II: Agent-Based Computational Economics, edited by Leigh Tesfatsion and Ken Judd , Elsevier, Amsterdam 2006," CeNDEF Working Papers 05-03, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    2. Mikhail Anufriev & Giulio Bottazzi, 2006. "Noisy Trading in the Large Market Limit," Lecture Notes in Economics and Mathematical Systems, in: M. Beckmann & H. P. Künzi & G. Fandel & W. Trockel & A. Basile & A. Drexl & H. Dawid & K. Inderfurth (ed.), Artificial Economics, pages 137-145, Springer.
    3. Anufriev, Mikhail & Bottazzi, Giulio & Pancotto, Francesca, 2006. "Equilibria, stability and asymptotic dominance in a speculative market with heterogeneous traders," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1787-1835.
    4. Mikhail Anufriev, 2008. "Wealth-driven competition in a speculative financial market: examples with maximizing agents," Quantitative Finance, Taylor & Francis Journals, vol. 8(4), pages 363-380.
    5. Sandrine Jacob Leal, 2015. "Fundamentalists, Chartists and Asset pricing anomalies," Post-Print hal-01508002, HAL.
    6. 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.
    7. Sandrine Jacob Leal, 2013. "Momentum effect in individual stocks and heterogeneous beliefs among fundamentalists," Economics Bulletin, AccessEcon, vol. 33(4), pages 3102-3116.
    8. Sandrine Jacob Leal, 2015. "Fundamentalists, chartists and asset pricing anomalies," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1837-1850, November.

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    Keywords

    Asset Pricing Model; CRRA Framework; Equilibria Market Line; Market Selection Principle;
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