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arXiv · 2301.09214

Pathwise stochastic control and a class of stochastic partial differential equations

Neeraj Bhauryal·Ana Bela Cruzeiro·Carlos Oliveira
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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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Neeraj Bhauryal, Ana Bela Cruzeiro, Carlos Oliveira. 2023-01-22. Pathwise stochastic control and a class of stochastic partial differential equations. https://arxiv.org/abs/2301.09214

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