Nonlinear Fokker-Planck equation in the model of asset returns

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1 Citation (Scopus)

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.

Original languageEnglish
Article number038
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume4
DOIs
Publication statusPublished - 6 Apr 2008

Keywords

  • Fokker-Planck equation
  • Non-linear evolution operator
  • Semiclassical asymptotics
  • The cauchy problem
  • Trajectory concentrated functions

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology
  • Mathematical Physics

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