Optimal control of infinite-dimensional differential systems with randomness and path-dependence and stochastic path-dependent Hamilton-Jacobi equations

2023/07/17 by Jinniao Qiu, Yang Yang, Qiu, Jinniao +1
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.2307.08882

Abstract

This paper is devoted to the stochastic optimal control problem of infinite-dimensional differential systems allowing for both path-dependence and measurable randomness. As opposed to the deterministic path-dependent cases studied by Bayraktar and Keller [J. Funct. Anal. 275 (2018), 2096--2161], the value function turns out to be a random field on the path space and it is characterized by a stochastic path-dependent Hamilton-Jacobi (SPHJ) equation. A notion of viscosity solution is proposed and the value function is proved to be the unique viscosity solution to the associated SPHJ equation.

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