Stochastic Optimization Theory of Backward Stochastic Differential Equations Driven by G-Brownian Motion

Stochastic Optimization Theory of Backward Stochastic Differential Equations Driven by G-Brownian Motion

We consider the stochastic optimal control problems under G-expectation. Based on the theory of backward stochastic differential equations driven by G-Brownian motion, which was introduced in Hu et al. (2012), we can investigate the more general stochastic optimal control problems under G-expectatio...

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Main Authors: Zhonghao Zheng, Xiuchun Bi, Shuguang Zhang
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/564524
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spelling doaj-d3a8e9fde9a6457aad4d1b3a6e2e09c12020-11-24T22:55:24ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/564524564524Stochastic Optimization Theory of Backward Stochastic Differential Equations Driven by G-Brownian MotionZhonghao Zheng0Xiuchun Bi1Shuguang Zhang2School of Mathematical Sciences, Xiamen University, Xiamen 361005, ChinaDepartment of Statistics and Finance, University of Science and Technology of China, Hefei 230026, ChinaDepartment of Statistics and Finance, University of Science and Technology of China, Hefei 230026, ChinaWe consider the stochastic optimal control problems under G-expectation. Based on the theory of backward stochastic differential equations driven by G-Brownian motion, which was introduced in Hu et al. (2012), we can investigate the more general stochastic optimal control problems under G-expectation than that were constructed in Zhang (2011). Then we obtain a generalized dynamic programming principle, and the value function is proved to be a viscosity solution of a fully nonlinear second-order partial differential equation.http://dx.doi.org/10.1155/2013/564524
collection DOAJ
language English
format Article
sources DOAJ
author Zhonghao Zheng
Xiuchun Bi
Shuguang Zhang
spellingShingle Zhonghao Zheng
Xiuchun Bi
Shuguang Zhang
Stochastic Optimization Theory of Backward Stochastic Differential Equations Driven by G-Brownian Motion
Abstract and Applied Analysis
author_facet Zhonghao Zheng
Xiuchun Bi
Shuguang Zhang
author_sort Zhonghao Zheng
title Stochastic Optimization Theory of Backward Stochastic Differential Equations Driven by G-Brownian Motion
title_short Stochastic Optimization Theory of Backward Stochastic Differential Equations Driven by G-Brownian Motion
title_full Stochastic Optimization Theory of Backward Stochastic Differential Equations Driven by G-Brownian Motion
title_fullStr Stochastic Optimization Theory of Backward Stochastic Differential Equations Driven by G-Brownian Motion
title_full_unstemmed Stochastic Optimization Theory of Backward Stochastic Differential Equations Driven by G-Brownian Motion
title_sort stochastic optimization theory of backward stochastic differential equations driven by g-brownian motion
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
description We consider the stochastic optimal control problems under G-expectation. Based on the theory of backward stochastic differential equations driven by G-Brownian motion, which was introduced in Hu et al. (2012), we can investigate the more general stochastic optimal control problems under G-expectation than that were constructed in Zhang (2011). Then we obtain a generalized dynamic programming principle, and the value function is proved to be a viscosity solution of a fully nonlinear second-order partial differential equation.
url http://dx.doi.org/10.1155/2013/564524
work_keys_str_mv AT zhonghaozheng stochasticoptimizationtheoryofbackwardstochasticdifferentialequationsdrivenbygbrownianmotion
AT xiuchunbi stochasticoptimizationtheoryofbackwardstochasticdifferentialequationsdrivenbygbrownianmotion
AT shuguangzhang stochasticoptimizationtheoryofbackwardstochasticdifferentialequationsdrivenbygbrownianmotion
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