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Pathwise stochastic control and a class of stochastic partial differential equations (2301.09214v2)
Published 22 Jan 2023 in math.PR, math.AP, and math.OC
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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