The Mean Field Forward Backward Stochastic Differential Equations and Stochastic Partial Differential Equations
Pure and Applied Mathematics Journal
Volume 4, Issue 3, June 2015, Pages: 120-127
Received: May 14, 2015; Accepted: May 26, 2015; Published: Jun. 6, 2015
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Authors
Jie Zhu, School of Information, Beijing Wuzi University, Beijing, China
Hong Zhang, School of Information, Beijing Wuzi University, Beijing, China
Li Zhou, School of Information, Beijing Wuzi University, Beijing, China
Yuhang Feng, Insurance Department, Central University of Finance and Economics, Beijing, China
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Abstract
Since 1990 Pardoux and Peng, proposed the theory of backward stochastic differential equation Backward stochastic differential equation and is backward stochastic differential equations (short for FBSDE) theory has been widely research (see El Karoui, Peng and Cauenez, Ma and Yong, etc.) Generally, a backward stochastic differential equation is a type Ito stochastic differential equation and a coupling Pardoux - Peng and backward stochastic differential equation. Antonelli, Ma, Protter and Yong is backward stochastic differential equation for a series of research, and apply to the financial. One of the research direction is put forward by Hu and Peng first. Peng and Wu Peng and Shi made a further research, and Yong to a more detailed discussion of this method, by introducing the concept of the bridge, systematically studied the FBSDE continuity method. Because such a system can be applied to random Feynman - Kac of partial differential equations of research, And a double optimal control problem of stochastic control systems, we will be working in Peng and Shi further in-depth study on the basis of this category are backward stochastic differential equation. In this paper, we are considering various constraint conditions with backward stochastic differential equation.
Keywords
FBSDE, Mean-Field Forward Backward, Stochastic Differential Equations, Stochastic Partial Differential Equations
To cite this article
Jie Zhu, Hong Zhang, Li Zhou, Yuhang Feng, The Mean Field Forward Backward Stochastic Differential Equations and Stochastic Partial Differential Equations, Pure and Applied Mathematics Journal. Vol. 4, No. 3, 2015, pp. 120-127. doi: 10.11648/j.pamj.20150403.20
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