Nonlinear Fokker-Planck Equation in the Model of Asset Returns

Details Nonlinear Fokker-Planck Equation in the Model of Asset Returns Nonlinear Fokker-Planck Equation in the Model of Asset Returns

2008-04-06

arxiv.org/abs/0804.0900v1

SIGMA 4 (2008), 038, 10 pages

Economy

Quantitative Finance

Computational Finance

This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (Ju

Scientific paper

10.3842/SIGMA.2008.038

The Fokker-Planck equation with diffusion coefficient quadratic in space variable, linear drift coefficient, and nonlocal nonlinearity term is considered in the framework of a model of analysis of asset returns at financial markets. For special cases of such a Fokker-Planck equation we describe a construction of exact solution of the Cauchy problem. In the general case, we construct the leading term of the Cauchy problem solution asymptotic in a formal small parameter in semiclassical approximation following the complex WKB-Maslov method in the class of trajectory concentrated functions.

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