Maximum principle for stochastic recursive optimal control problem under model uncertainty

TL;DR

This paper develops a stochastic maximum principle for recursive optimal control problems under model uncertainty, using linearization and weak convergence methods, and applies it to a linear quadratic robust control problem.

Contribution

It introduces a maximum principle for stochastic recursive control under model uncertainty, extending existing theories with new analytical techniques.

Findings

Derived a stochastic maximum principle for the problem.

Applied the principle to a linear quadratic robust control case.

Provided theoretical foundations for control under uncertainty.

Abstract

In this paper, we consider a stochastic recursive optimal control problem under model uncertainty. In this framework, the cost function is described by solutions of a family of backward stochastic differential equations. With the help of the linearization techniques and weak convergence methods, we derive the corresponding stochastic maximum principle. Moreover, a linear quadratic robust control problem is also studied.