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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| Дата: | 2008 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2008
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149046 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1490462019-02-20T01:28:39Z Nonlinear Fokker-Planck Equation in the Model of Asset Returns Shapovalov, A. Trifonov, A. Masalova, E. 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. 2008 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/149046 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Shapovalov, A. Trifonov, A. Masalova, E. |
| spellingShingle |
Shapovalov, A. Trifonov, A. Masalova, E. Nonlinear Fokker-Planck Equation in the Model of Asset Returns Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Shapovalov, A. Trifonov, A. Masalova, E. |
| author_sort |
Shapovalov, A. |
| title |
Nonlinear Fokker-Planck Equation in the Model of Asset Returns |
| title_short |
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_sort |
nonlinear fokker-planck equation in the model of asset returns |
| publisher |
Інститут математики НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149046 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT shapovalova nonlinearfokkerplanckequationinthemodelofassetreturns AT trifonova nonlinearfokkerplanckequationinthemodelofassetreturns AT masalovae nonlinearfokkerplanckequationinthemodelofassetreturns |
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2023-05-20T17:32:04Z |
| last_indexed |
2023-05-20T17:32:04Z |
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