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.
Highlights
Nonlinear BSDEs in the framework of linear expectation were introduced by Pardoux and Peng [1] in 1990
We investigate the stochastic optimal control problems with a BSDE driven by G-Brownian motion constructed in [19, 20] as cost function
We introduce the setting for stochastic optimal control problems under G-expectation
Summary
Nonlinear BSDEs in the framework of linear expectation were introduced by Pardoux and Peng [1] in 1990. An important application of BSDEs is that we can define the recursive utility functions from BSDEs, which can index scaling risks in the study of economics and finance [21,22,23,24] Based on these results, a type of significant stochastic optimal control problems under linear expectation with a BSDE as cost function was studied [2, 4, 7,8,9]. We investigate the stochastic optimal control problems with a BSDE driven by G-Brownian motion constructed in [19, 20] as cost function.
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