Kinetic models for socio-economic dynamics of speculative markets

In this paper we introduce a simple model for a financial market characterized by a single stock or good and an interplay between two different traders populations, chartists and fundamentalists, which determine the price dynamic of the stock. The model has been inspired by the microscopic Lux-Marchesi model (T.Lux, M.Marchesi, Nature 397, (1999), 498--500). The introduction of kinetic equations permits to study the asymptotic behavior of the investments and the price distributions and to characterize the regimes of lognormal behavior and the formation of power law tails.

[1]  Lorenzo Pareschi,et al.  On a Kinetic Model for a Simple Market Economy , 2004, math/0412429.

[2]  G. Toscani,et al.  Self-Similarity and Power-Like Tails in Nonconservative Kinetic Models , 2010, 1009.2760.

[3]  S. Redner,et al.  Wealth distributions in asset exchange models , 1998, 1006.4595.

[4]  Sorin Solomon,et al.  Theoretical analysis and simulations of the generalized Lotka-Volterra model. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  R. Lourie,et al.  The Statistical Mechanics of Financial Markets , 2002 .

[6]  A. Tversky,et al.  Choices, Values, and Frames , 2000 .

[7]  J. Marchal.  Cours d'economie politique , 1950 .

[8]  L. Pareschi,et al.  Price dynamics in financial markets: a kinetic approach , 2010, 1007.1631.

[9]  Lorenzo Pareschi,et al.  Mesoscopic Modelling of Financial Markets , 2009, 1009.2743.

[10]  Giuseppe Toscani,et al.  Hydrodynamics from Kinetic Models of Conservative Economies , 2007 .

[11]  Moshe Levy,et al.  Microscopic Simulation of Financial Markets , 2000 .

[12]  Adrian Pagan,et al.  The econometrics of financial markets , 1996 .

[13]  G. Toscani,et al.  Kinetic models of opinion formation , 2006 .

[14]  L. Pareschi,et al.  Microscopic and Kinetic Models in Financial Markets , 2010 .

[15]  H. Eugene Stanley,et al.  Econophysics: Two-phase behaviour of financial markets , 2003, Nature.

[16]  T. Lux.  The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions , 1998 .

[17]  Rosario N. Mantegna,et al.  Book Review: An Introduction to Econophysics, Correlations, and Complexity in Finance, N. Rosario, H. Mantegna, and H. E. Stanley, Cambridge University Press, Cambridge, 2000. , 2000 .

[18]  Bikas K. Chakrabarti,et al.  Pareto Law in a Kinetic Model of Market with Random Saving Propensity , 2004 .

[19]  M. Marchesi,et al.  VOLATILITY CLUSTERING IN FINANCIAL MARKETS: A MICROSIMULATION OF INTERACTING AGENTS , 1998 .

[20]  M. Mézard,et al.  Wealth condensation in a simple model of economy , 2000, cond-mat/0002374.

[21]  Lorenzo Pareschi,et al.  An introduction to Monte Carlo method for the Boltzmann equation , 2001 .

[22]  M. Marchesi,et al.  VOLATILITY CLUSTERING IN FINANCIAL MARKETS: A MICROSIMULATION OF INTERACTING AGENTS , 2000 .

[23]  Dietrich Stauffer,et al.  Microscopic models of financial markets , 2001, cond-mat/0110354.

[24]  J. Bouchaud,et al.  Herd Behavior and Aggregate Fluctuations in Financial Markets , 1997 .

[25]  R. Illner,et al.  The mathematical theory of dilute gases , 1994 .

[26]  Giuseppe Toscani,et al.  On Steady Distributions of Kinetic Models of Conservative Economies , 2008 .

[27]  S. Solomon,et al.  A microscopic model of the stock market: Cycles, booms, and crashes , 1994 .

[28]  Bikas K. Chakrabarti,et al.  Statistical mechanics of money: how saving propensity affects its distribution , 2000, cond-mat/0004256.

[29]  Lorenzo Pareschi,et al.  Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences , 2010 .

[30]  V. Plerou,et al.  A theory of power-law distributions in financial market fluctuations , 2003, Nature.

[31]  A. Tversky,et al.  Prospect theory: an analysis of decision under risk — Source link , 2007 .

[32]  A. Tversky,et al.  Prospect Theory : An Analysis of Decision under Risk Author ( s ) : , 2007 .

[33]  F. Slanina.  Inelastically scattering particles and wealth distribution in an open economy. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  Victor M. Yakovenko,et al.  Statistical mechanics of money , 2000 .

[35]  S. Prabakaran,et al.  THE STATISTICAL MECHANICS OF FINANCIAL MARKETS , 2007 .

[36]  Sorin Solomon,et al.  STOCHASTIC LOTKA-VOLTERRA SYSTEMS OF COMPETING AUTO-CATALYTIC AGENTS LEAD GENERICALLY TO TRUNCATED PARETO POWER WEALTH DISTRIBUTION, TRUNCATED LEVY DISTRIBUTION OF MARKET RETURNS, CLUSTERED VOLATILITY, BOOMS AND CRACHES * , 1998, cond-mat/9803367.

[37]  M. Marchesi,et al.  Scaling and criticality in a stochastic multi-agent model of a financial market , 1999, Nature.