Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2014 (2014), Article ID 262713, 17 pages.
Backward Stochastic Differential Equations Coupled with Value Function and Related Optimal Control Problems
We get a new type of controlled backward stochastic differential equations (BSDEs), namely, the BSDEs, coupled with value function. We prove the existence and the uniqueness theorem as well as a comparison theorem for such BSDEs coupled with value function by using the approximation method. We get the related dynamic programming principle (DPP) with the help of the stochastic backward semigroup which was introduced by Peng in 1997. By making use of a new, more direct approach, we prove that our nonlocal Hamilton-Jacobi-Bellman (HJB) equation has a unique viscosity solution in the space of continuous functions of at most polynomial growth. These results generalize the corresponding conclusions given by Buckdahn et al. (2009) in the case without control.
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 262713, 17 pages.
First available in Project Euclid: 2 October 2014
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Hao, Tao; Li, Juan. Backward Stochastic Differential Equations Coupled with Value Function and Related Optimal Control Problems. Abstr. Appl. Anal. 2014 (2014), Article ID 262713, 17 pages. doi:10.1155/2014/262713. https://projecteuclid.org/euclid.aaa/1412273262