Pathwise stochastic control and a class of stochastic partial differential equations

2023/01/22 by Neeraj Bhauryal, Bhauryal, Neeraj, Ana Bela Cruzeiro +3
Decision Sciences · Economics, Econometrics and Finance · #35D40 #60H15 #93E20 #Analysis of PDEs (math.AP) #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2301.09214

openalex publication_date 2023/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We consider a pathwise stochastic optimal control problem and study the associated (not necessarily adapted) Hamilton-Jacobi-Bellman stochastic partial differential equation. We show that the value process is the unique solution of this equation, in the viscosity sense. Finally, we discuss a version of some corresponding stochastic pathwise Noether theorem.

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