Fluctuations of stock price model by statistical physics systems

We investigate the statistical properties of fluctuations of the stock price process in a stock market by the interacting stochastic systems. The theory of the random continuum percolation is applied to construct a financial model that describes the behavior of a stock price, and the continuum percolation is used to describe the ''herd effect'' of investors in a stock market. Further, the statistical physics model is applied to model and study the stock price. In this paper, we discuss the asymptotical behavior of the distributions for this stock price process, and show the convergence of the finite dimensional probability distributions for the financial model.

[1]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[2]  T. Liggett.  Interacting Particle Systems , 1985 .

[3]  Bernard Lapeyre,et al.  Introduction to Stochastic Calculus Applied to Finance , 2007 .

[4]  R. Bass,et al.  Review: P. Billingsley, Convergence of probability measures , 1971 .

[5]  Hisatoshi Tanaka.  A Percolation Model of Stock Price Fluctuations , 2002 .

[6]  R. Ellis,et al.  Entropy, large deviations, and statistical mechanics , 1985 .

[7]  Jun Wang.  The statistical properties of the interfaces for the lattice Widom-Rowlinson model , 2006, Appl. Math. Lett..

[8]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[9]  Andrzej Krawiecki,et al.  Microscopic Spin Model For The Stock Market With Attractor Bubbling And Heterogeneous Agents , 2005 .

[10]  Valery A. Kholodnyi.  Valuation and dynamic replication of contingent claims in the framework of the beliefs-preferences gauge symmetry , 2002 .

[11]  Roberto Renò,et al.  Threshold Bipower Variation and the Impact of Jumps on Volatility Forecasting , 2008 .

[12]  Jun Wang.  The estimates of correlations in two-dimensional Ising model , 2009 .

[13]  Yacine Aït-Sahalia,et al.  Disentangling diffusion from jumps , 2004 .

[14]  Davide Pirino,et al.  Jump detection and long range dependence , 2009 .

[15]  N. Shephard,et al.  Power and bipower variation with stochastic volatility and jumps , 2003 .

[16]  R. Renò,et al.  Threshold Estimation of Jump-Diffusion Models and Interest Rate Modeling , 2008 .

[17]  A. Si,et al.  Entropy,Large Deviations,and Statistical Mechanics , 2011 .

[18]  E. Olivieri,et al.  Large deviations and metastability: Large deviations and statistical mechanics , 2005 .

[19]  Dietrich Stauffer,et al.  Crossover in the Cont–Bouchaud percolation model for market fluctuations , 1998 .

[20]  Jun Wang.  RANDOM WALK ON THE POISSON POINTS OF INFINITE CLUSTER OF THE CONTINUOUS PERCOLATION , 1998 .

[21]  Terence C. Mills.  The Econometric Modelling of Financial Time Series: Regression techniques for non-integrated financial time series , 1999 .

[22]  Joushin Murai.  The Dobrushin-Hryniv theory for the two-dimensional latttice Widom-Rowlinson model , 2004 .