Maximum principle for discrete-time robust stochastic optimal control problem

2025/08/24 by He, Wei
#60H30 #93C55 #93E20 #FOS: Mathematics #G.3 #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.2508.17249

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.

Citations

• Maximum principle for discrete-time stochastic optimal control problem under distribution uncertainty
• Distributionally Robust Markov Decision Processes and their Connection to Risk Measures
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