Discrete-time approximation for stochastic optimal control problems under the $G$-expectation framework

TL;DR

This paper introduces discrete-time approximation schemes for stochastic optimal control problems within the $G$-expectation framework, demonstrating their convergence and effectiveness through numerical examples.

Contribution

It presents a novel recursive discrete-time scheme for $G$-expectation-based control problems and proves its convergence and rate, advancing numerical methods in this area.

Findings

Convergence of the proposed schemes is established.

Convergence rates are explicitly determined.

Numerical examples confirm the effectiveness of the schemes.

Abstract

In this paper, we propose a class of discrete-time approximation schemes for stochastic optimal control problems under the $G$-expectation framework. The proposed schemes are constructed recursively based on piecewise constant policy. We prove the convergence of the discrete schemes and determine the convergence rates. Several numerical examples are presented to illustrate the effectiveness of the obtained results.