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

Abstract

In this paper, 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 [10.11], we can investigate the more general stochastic optimal control problems under G-expectation than that were constructed in [28]. 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.

25 pages

References in corpus (4)

• A theoretical framework for the pricing of contingent claims in the presence of model uncertainty
• A Complete Representation Theorem for $G$-martingales
• Backward Stochastic Differential Equations Driven by G-Brownian Motion
• Comparison Theorem, Feynman-Kac Formula and Girsanov Transformation for BSDEs Driven by G-Brownian Motion