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Non-local Hamilton-Jacobi-Bellman equations for the stochastic optimal control of path-dependent piecewise deterministic processes (2408.02147v1)
Published 4 Aug 2024 in math.PR, math.AP, and math.OC
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.