**Nonlinear Fokker-Planck-Kolmogorov equation in analysis of asset returns**

**Abstract:**

We consider the nonlinear Fokker-Planck-Kolmogorov equation (FPKE) coefficients of which depend on the first
moment of the FPKE solution. For the FPKE with constant dispersion and nonlinear drift, an exact evolution operator is
constructed and symmetry properties are discussed. The evolution operator is used to construct a solution of the Cauchy
problem in the semiclassical approximation for the FPKE with time-dependent dispersion quadratic in coordinates. An
example related to distribution of increments of asset prices on financial markets is considered and properties of the
distributions with 'power law'
and 'heavy tails' are discussed.