Relationship between MP and DPP for stochastic recursive optimal control problem under volatility uncertainty

2022/10/11 by Xiaojuan Li, Li, Xiaojuan
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #35K15 #60H10 #93E20 #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2210.05213

openalex publication_date 2022/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the relationship between maximum principle (MP) and dynamic programming principle (DPP) for stochastic recursive optimal control problem driven by G-Brownian motion. Under the smooth assumption for the value function, we obtain the connection between MP and DPP under a reference probability P_t,x^∗. Within the framework of viscosity solution, we establish the relation between the first-order super-jet, sub-jet of the value function and the solution to the adjoint equation respectively.

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