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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 564524, 11 pages
http://dx.doi.org/10.1155/2013/564524
Research Article

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

1School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
2Department of Statistics and Finance, University of Science and Technology of China, Hefei 230026, China

Received 15 June 2013; Accepted 19 July 2013

Academic Editor: Massimiliano Ferrara

Copyright © 2013 Zhonghao Zheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.