Nonlinear Fokker-Planck Equation in the Model of Asset Returns
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 co...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2008 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2008
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149046 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Nonlinear Fokker-Planck Equation in the Model of Asset Returns / A. Shapovalov, A. Trifonov, E. Masalova // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 16 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862688740144578560 |
|---|---|
| author | Shapovalov, A. Trifonov, A. Masalova, E. |
| author_facet | Shapovalov, A. Trifonov, A. Masalova, E. |
| citation_txt | Nonlinear Fokker-Planck Equation in the Model of Asset Returns / A. Shapovalov, A. Trifonov, E. Masalova // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 16 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-07T16:09:55Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-149046 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:09:55Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Shapovalov, A. Trifonov, A. Masalova, E. 2019-02-19T13:17:15Z 2019-02-19T13:17:15Z 2008 Nonlinear Fokker-Planck Equation in the Model of Asset Returns / A. Shapovalov, A. Trifonov, E. Masalova // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 16 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 35K55; 62M10; 91B28; 91B84 https://nasplib.isofts.kiev.ua/handle/123456789/149046 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. The work was supported by the President of the Russian Federation, Grant No SS-871.2008.2 and Grant of the RFBR No 07-01-08035. A. Shapovalov acknowledges the partial support from the International Mathematical Union for participation in the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics”. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Nonlinear Fokker-Planck Equation in the Model of Asset Returns Article published earlier |
| spellingShingle | Nonlinear Fokker-Planck Equation in the Model of Asset Returns Shapovalov, A. Trifonov, A. Masalova, E. |
| title | Nonlinear Fokker-Planck Equation in the Model of Asset Returns |
| title_full | Nonlinear Fokker-Planck Equation in the Model of Asset Returns |
| title_fullStr | Nonlinear Fokker-Planck Equation in the Model of Asset Returns |
| title_full_unstemmed | Nonlinear Fokker-Planck Equation in the Model of Asset Returns |
| title_short | Nonlinear Fokker-Planck Equation in the Model of Asset Returns |
| title_sort | nonlinear fokker-planck equation in the model of asset returns |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149046 |
| work_keys_str_mv | AT shapovalova nonlinearfokkerplanckequationinthemodelofassetreturns AT trifonova nonlinearfokkerplanckequationinthemodelofassetreturns AT masalovae nonlinearfokkerplanckequationinthemodelofassetreturns |