### 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 language | English |
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Article number | 038 |

Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |

Volume | 4 |

DOIs | |

Publication status | Published - 6 Apr 2008 |

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### 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

### Cite this

**Nonlinear Fokker-Planck equation in the model of asset returns.** / Shapovalov, Aleksandr Vasilievich; Trifonov, Andrey; Masalova, Elena.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Nonlinear Fokker-Planck equation in the model of asset returns

AU - Shapovalov, Aleksandr Vasilievich

AU - Trifonov, Andrey

AU - Masalova, Elena

PY - 2008/4/6

Y1 - 2008/4/6

N2 - 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.

AB - 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.

KW - Fokker-Planck equation

KW - Non-linear evolution operator

KW - Semiclassical asymptotics

KW - The cauchy problem

KW - Trajectory concentrated functions

UR - http://www.scopus.com/inward/record.url?scp=84857344199&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84857344199&partnerID=8YFLogxK

U2 - 10.3842/SIGMA.2008.038

DO - 10.3842/SIGMA.2008.038

M3 - Article

AN - SCOPUS:84857344199

VL - 4

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SN - 1815-0659

M1 - 038

ER -