Dynamic programming principle for stochastic optimal control problem under degenerate G-expectation

TL;DR

This paper establishes a dynamic programming principle for stochastic optimal control problems under degenerate G-expectation, proving the value function's determinism and its characterization as a unique viscosity solution to the HJB equation.

Contribution

It introduces an approximation method for admissible controls and proves the value function's properties under degenerate G-expectation, extending existing theory.

Findings

Value function is deterministic under degenerate G-expectation.

Dynamic programming principle is established for the control problem.

Value function uniquely solves the associated HJB equation.

Abstract

In this paper, we study a stochastic optimal control problem under degenerate G-expectation. By using implied partition method, we show that the approximation result for admissible controls still hold. Based on this result, we prove that the value function is deterministic, and obtain the dynamic programming principle. Furthermore, we prove that the value function is the unique viscosity solution to the related HJB equation under degenerate case.