Relationship between MP and DPP for stochastic recursive optimal control problem under volatility uncertainty

TL;DR

This paper explores the connection between the maximum principle and dynamic programming principle in stochastic recursive optimal control problems driven by G-Brownian motion, establishing relations under smoothness and viscosity solution frameworks.

Contribution

It provides a novel link between MP and DPP for G-Brownian motion driven control problems, including relations involving viscosity solutions and adjoint equations.

Findings

Established the connection between MP and DPP under smooth value functions.

Linked the super-jet and sub-jet of the value function to the adjoint equation.

Extended the relationship to viscosity solutions framework.

Abstract

In this paper, we study the relationship between maximum principle (MP) and dynamic programming principle (DPP) for stochastic recursive optimal control problem driven by $G$-Brownian motion. Under the smooth assumption for the value function, we obtain the connection between MP and DPP under a reference probability $P_{t,x}^{\ast}$. Within the framework of viscosity solution, we establish the relation between the first-order super-jet, sub-jet of the value function and the solution to the adjoint equation respectively.