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

TL;DR

This paper develops a stochastic optimal control framework under G-expectation using backward stochastic differential equations driven by G-Brownian motion, leading to a generalized dynamic programming principle and a nonlinear PDE characterization.

Contribution

It introduces a generalized stochastic control approach under G-expectation and proves the value function as a viscosity solution to a nonlinear PDE.

Findings

Established a dynamic programming principle under G-expectation.

Proved the value function is a viscosity solution of a fully nonlinear PDE.

Extended the 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.