Controlled ordinary differential equations with random path-dependent coefficients and stochastic path-dependent Hamilton–Jacobi equations

Jinniao Qiu

Stochastic Processes and their Applications, 2022, vol. 154, issue C, 1-25

Abstract: This paper is devoted to the stochastic optimal control problem of ordinary differential equations allowing for both path-dependence and measurable randomness. As opposed to the deterministic path-dependent cases, 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.

Keywords: Stochastic path-dependent Hamilton–Jacobi equation; Stochastic optimal control; Viscosity solution; Backward stochastic partial differential equation (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:154:y:2022:i:c:p:1-25

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DOI: 10.1016/j.spa.2022.09.001

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