Abstract and Applied Analysis

Backward Stochastic Differential Equations Coupled with Value Function and Related Optimal Control Problems

Tao Hao and Juan Li

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 262713, 17 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412273262

Digital Object Identifier
doi:10.1155/2014/262713

Mathematical Reviews number (MathSciNet)
MR3191027

Zentralblatt MATH identifier
07022039

Citation

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


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