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Nonlinear Fokker-Planck Equation in the Model of Asset Returns
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2008, том 4
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Nonlinear Fokker-Planck Equation in the Model of Asset Returns
Інший ID:
2000 Mathematics Subject Classification: 35K55; 62M10; 91B28; 91B84
Посилання:
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.
Підтримка:
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”.
Дата:
2008
Переглядів:
439
Завантажень:
253
Анотація:
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.
