Stochastic optimal control problem with infinite horizon driven by G-Brownian motion

TL;DR

This paper investigates an infinite horizon stochastic optimal control problem driven by G-Brownian motion, establishing the value function's regularity, dynamic programming principle, and its characterization as a viscosity solution of the HJBI equation.

Contribution

It introduces a novel framework for control problems under G-Brownian motion, proving key properties of the value function and linking it to the HJBI equation.

Findings

Value function is regular and unique.

Dynamic programming principle holds.

Value function solves the HJBI equation as a viscosity solution.

Abstract

The present paper considers a stochastic optimal control problem, in which the cost function is defined through a backward stochastic differential equation with infinite horizon driven by G-Brownian motion. Then we study the regularities of the value function and establish the dynamic programming principle. Moreover, we prove that the value function is the uniqueness viscosity solution of the related HJBI equation.