Nonlinear Fokker–Planck Equation in the Model of Asset Returns

Alexander Shapovalov ; Andrey Trifonov ; Elena Masalova

Symmetry, integrability and geometry: methods and applications, Tome 4 (2008)

Résumé

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.

Détail

Keywords: Fokker–Planck equation; semiclassical asymptotics; the Cauchy problem; nonlinear evolution operator; trajectory concentrated functions.

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