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

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 t...

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Main Authors: Tao Hao, Juan Li
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/262713
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spelling doaj-90bf0eee7c6642e3be326dc8120c2ca92020-11-24T23:58:09ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/262713262713Backward Stochastic Differential Equations Coupled with Value Function and Related Optimal Control ProblemsTao Hao0Juan Li1School of Mathematics and Statistics, Shandong University, Weihai 264209, ChinaSchool of Mathematics and Statistics, Shandong University, Weihai 264209, ChinaWe 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.http://dx.doi.org/10.1155/2014/262713
collection DOAJ
language English
format Article
sources DOAJ
author Tao Hao
Juan Li
spellingShingle Tao Hao
Juan Li
Backward Stochastic Differential Equations Coupled with Value Function and Related Optimal Control Problems
Abstract and Applied Analysis
author_facet Tao Hao
Juan Li
author_sort Tao Hao
title Backward Stochastic Differential Equations Coupled with Value Function and Related Optimal Control Problems
title_short Backward Stochastic Differential Equations Coupled with Value Function and Related Optimal Control Problems
title_full Backward Stochastic Differential Equations Coupled with Value Function and Related Optimal Control Problems
title_fullStr Backward Stochastic Differential Equations Coupled with Value Function and Related Optimal Control Problems
title_full_unstemmed Backward Stochastic Differential Equations Coupled with Value Function and Related Optimal Control Problems
title_sort backward stochastic differential equations coupled with value function and related optimal control problems
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
description 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.
url http://dx.doi.org/10.1155/2014/262713
work_keys_str_mv AT taohao backwardstochasticdifferentialequationscoupledwithvaluefunctionandrelatedoptimalcontrolproblems
AT juanli backwardstochasticdifferentialequationscoupledwithvaluefunctionandrelatedoptimalcontrolproblems
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