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arXiv · 0804.0900

Nonlinear Fokker-Planck Equation in the Model of Asset Returns

Alexander Shapovalov·Andrey Trifonov·Elena Masalova
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Abstract

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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Alexander Shapovalov, Andrey Trifonov, Elena Masalova. 2008-04-06. Nonlinear Fokker-Planck Equation in the Model of Asset Returns. https://doi.org/10.3842/sigma.2008.038

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