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Proceedings Paper

Speculative equilibria and asymptotic dominance in a market with adaptive CRRA traders
Author(s): Mikhail Anufriev; Giulio Bottazzi; Francesca Pancotto
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Paper Abstract

We consider a simple pure exchange economy with two assets, one riskless, yielding a constant return on investment, and one risky, paying a stochastic dividend. Trading takes place in discrete time and in each trading period the price of the risky asset is fixed through the market clearing condition. Individual demands are expressed as fractions of traders wealth and depend on traders forecasts about future price movement. Under these assumptions, we derive the stochastic dynamical system that describes the evolution of price and wealth. We study the cases in which one or two agents operate in the market, identifying the possible equilibria and discussing their stability conditions. The main novelty of this paper rests in the abstraction from the precise characterization of agents' beliefs and preferences. In this respect our results generalize several previous contributions in the field. In particular, we show that, irrespectively of agents' behavior, the system can only possess isolated generic equilibria where a single agent dominates the market and continuous manifolds of non-generic equilibria where heterogeneous agents hold finite shares of the aggregate wealth. Moreover, we show that all possible equilibria belong to a one dimensional "Equilibria Market Line". Finally we discuss the role of different parameters for the stability of equilibria and the selection principle governing market dynamics.

Paper Details

Date Published: 23 May 2005
PDF: 15 pages
Proc. SPIE 5848, Noise and Fluctuations in Econophysics and Finance, (23 May 2005); doi: 10.1117/12.619471
Show Author Affiliations
Mikhail Anufriev, Sant'Anna School for Advanced Studies (Italy)
Giulio Bottazzi, Sant'Anna School for Advanced Studies (Italy)
Francesca Pancotto, Sant'Anna School for Advanced Studies (Italy)

Published in SPIE Proceedings Vol. 5848:
Noise and Fluctuations in Econophysics and Finance
Derek Abbott; Jean-Philippe Bouchaud; Xavier Gabaix; Joseph L. McCauley, Editor(s)

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