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

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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

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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.

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Paper provided by Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy in its series LEM Papers Series with number 2005/06.

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Date of creation: 29 Apr 2005
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Handle: RePEc:ssa:lemwps:2005/06

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This paper has been announced in the following NEP Reports:

NEP-ALL-2005-05-14 (All new papers)
NEP-FIN-2005-05-14 (Finance)

References listed on IDEAS
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Amir, Rabah & Evstigneev, Igor V. & Hens, Thorsten & Schenk-Hoppe, Klaus Reiner, 2005. "Market selection and survival of investment strategies," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 105-122, February. [Downloadable!] (restricted)
Other versions:
- R Amir & I Evstigneev & T Hens & K R Schenk-Hoppé, 2002. "Market Selection and Survival of Investment Strategies," The School of Economics Discussion Paper Series 0215, Economics, The University of Manchester. [Downloadable!]
- Rabah Amir & Igor V. Evstigneev & Thorsten Hens & Klaus Reiner Schenk-Hoppé, 2002. "Market Selection and Survival of Investment Strategies," Discussion Papers 02-16, University of Copenhagen. Department of Economics. [Downloadable!]
- Rabah Amir & Igor V. Evstigneev & Thorsten Hens & Klaus Reiner Schenk-Hoppé, . "Market Selection and Survival of Investment Strategies," IEW - Working Papers iewwp091, Institute for Empirical Research in Economics - IEW. [Downloadable!]
Carl Chiarella & Xue-Zhong He, 2001. "Asset Price and Wealth Dynamics Under Heterogeneous Expectations," Research Paper Series 56, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
Other versions:
- Xue-Zhong (Tony) He & Carl Chiarella, 2001. "Asset Price and Wealth Dynamics under Heterogeneous Expectations," CeNDEF Workshop Papers, January 2001 5A.2, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
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. [Downloadable!] (restricted)
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. [Downloadable!] (restricted)
Other versions:
- Thorsten Hens & Klaus Reiner Schenk-Hoppé, 2003. "Evolutionary Stability of Portfolio Rules in Incomplete Markets," Discussion Papers 03-03, University of Copenhagen. Department of Economics. [Downloadable!]
repec:isu:genres:2051 is not listed on IDEAS
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.
Other versions:
- Carl Chiarella & Xue-Zhong He, 2002. "An Adaptive Model on Asset Pricing and Wealth Dynamics with Heterogeneous Trading Strategies," Research Paper Series 84, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
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. [Downloadable!] (restricted)
Cars H. Hommes, 2005. "Heterogeneous Agent Models in Economics and Finance," Tinbergen Institute Discussion Papers 05-056/1, Tinbergen Institute. [Downloadable!]
Other versions:
- 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. [Downloadable!] (restricted)
De Long, J Bradford, et al, 1991. "The Survival of Noise Traders in Financial Markets," Journal of Business, University of Chicago Press, vol. 64(1), pages 1-19, January. [Downloadable!] (restricted)
Other versions:
- J. Bradford De Long & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann, 1988. "The Survival of Noise Traders in Financial Markets," NBER Working Papers 2715, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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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. [Downloadable!]

Full references

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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

Mikhail Anufriev, 2005. "Wealth-Driven Competition in a Speculative Financial Market: Examples with Maximizing Agents," LEM Papers Series 2005/27, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy. [Downloadable!]
Other versions:
- Anufriev, M., 2005. "Wealth-Driven Competition in a Speculative Financial Market: Examples With Maximizing Agents," CeNDEF Working Papers 05-17, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance. [Downloadable!]

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