Maximum principle for discrete-time robust stochastic optimal control problem

TL;DR

This paper establishes necessary and sufficient conditions for discrete-time robust stochastic optimal control problems with convex control domains, using a novel approach that handles the inf sup structure and provides explicit solutions in an investment context.

Contribution

It introduces a new variational inequality framework for inf sup problems in discrete-time stochastic control, overcoming limitations of classical methods.

Findings

Derived necessary and sufficient optimality conditions

Developed a variational inequality approach using weak convergence and minimax theorem

Provided explicit optimal control for a robust investment problem

Abstract

This paper firstly presents the necessary and sufficient conditions for a kind of discrete-time robust stochastic optimal control problem with convex control domains. As it is an "inf sup problem", the classical variational method is invalid. We obtain the variational inequality with a common reference probability by systematically using weak convergence approach and the minimax theorem. Moreover, a discrete-time robust investment problem is also studied where the explicit optimal control is given.