Nonlinear Fokker-Planck Equation in the Model of Asset Returns - Shapovalov, A.; Trifonov, A.; Masalova, E. (Symmetry, Integrability and Geometry: Methods and Applications, 2008)
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.