Backward stochastic differential equations coupled with value function and related optimal control problems
type: Item
instance of: scholarly article
title: Backward stochastic differential equations coupled with value function and related optimal control problems
zbMATH Open document ID: 1469.60185
DOI: 10.1155/2014/262713
author: Tao Hao
author: Juan Li
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: 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 \textit{S. Peng} [SIAM J. Control Optim. 28, No. 4, 966--979 (1990; Zbl 0712.93067)]. 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 \textit{R. Buckdahn} et al. [Ann. Probab. 37, No. 4, 1524--1565 (2009; Zbl 1176.60042)] in the case without control.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 49K45
Mathematics Subject Classification ID: 93E20
zbMATH DE Number: 7022039
zbMATH Keywords: controlled backward stochastic differential equations
zbMATH Keywords: stochastic backward semigroup
Wikidata QID: Q59037237
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/262713
OpenAlex ID: W2008721731
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description: scientific article; zbMATH DE number 7022039