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

Elena Bandini and Christian Keller

Stochastic Processes and their Applications, 2026, vol. 192, issue C

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.

Keywords: Path-dependent piecewise deterministic processes; Non-local path-dependent HJB equations; Stochastic optimal control (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1016/j.spa.2025.104813

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