Nonlinear Fokker-Planck equation in the model of asset returns

DOI10.3842/SIGMA.2008.038zbMATH Open1166.35340arXiv0804.0900OpenAlexW2158304612MaRDI QIDQ935738

Elena Masalova, A. V. Shapovalov, A. Yu. Trifonov

Publication date: 8 August 2008

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/0804.0900

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zbMATH Keywords

Fokker-Planck equationsemiclassical asymptoticsthe Cauchy problemnonlinear evolution operatortrajectory concentrated functions

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Auctions, bargaining, bidding and selling, and other market models (91B26) Initial value problems for second-order parabolic equations (35K15)

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