Non-local Hamilton-Jacobi-Bellman equations for the stochastic optimal control of path-dependent piecewise deterministic processes

Abstract

We study the optimal control of path-dependent piecewise deterministic processes. An appropriate dynamic programming principle is established. We prove that the associated value function is the unique minimax solution of the corresponding non-local path-dependent Hamilton-Jacobi-Bellman equation. This is the first well-posedness result for nonsmooth solutions of fully nonlinear non-local path-dependent partial differential equations.

Accepted by Stochastic Processes and Their Applications

References in corpus (5)

• On viscosity solutions of path dependent PDEs
• Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part II
• Viability, Invariance and Reachability for Controlled Piecewise Deterministic Markov Processes Associated to Gene Networks
• Path-Dependent Hamilton--Jacobi Equations: The Minimax Solutions Revised
• Optimal Liquidation under Partial Information with Price Impact