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

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  • Giulio Bottazzi
  • Mikhail Anufriev

    ()
    (Laboratory of Economic and Management Scuola Superiore Sant'Anna)

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. We describe the evolution of price and wealth distribution in the general case where any number of heterogeneous traders is allowed to operate in the market and any smooth function which maps the infinite information set to the present investment choice is allowed as agent's trading strategy. We give a complete characterization of equilibria and derive stability conditions analyzing a dynamical system of arbitrary large dimension. We show that this system 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. Irrespectively of agents number and of their behavior, we show that all possible equilibria returns belong to a one dimensional ``Equilibria Market Line''. Our general result extends previous contributions and allows a better understanding of the selection principle governing the asymptotic market dynamics

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2005 with number 375.

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Date of creation: 11 Nov 2005
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Handle: RePEc:sce:scecf5:375

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Keywords: Asset pricing; Price and wealth dynamics; Optimal selection principle.;

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  1. 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.
  2. C. Chiarella & X-Z. He, 2001. "Asset price and wealth dynamics under heterogeneous expectations," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 509-526.
  3. Chiarella, Carl & He, Xue-Zhong, 2002. "Heterogeneous Beliefs, Risk and Learning in a Simple Asset Pricing Model," Computational Economics, Society for Computational Economics, vol. 19(1), pages 95-132, February.
  4. Levy, Moshe & Levy, Haim & Solomon, Sorin, 1994. "A microscopic model of the stock market : Cycles, booms, and crashes," Economics Letters, Elsevier, vol. 45(1), pages 103-111, May.
  5. Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942, September.
  6. 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.
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Cited by:
  1. 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.

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