2025/11/10 by Yuan Cao, Cao, Yuchen, Jiongmin Yong +1
Computer Science · Economics, Econometrics and Finance · #49L25 #49N25 #93C27 #93E20 #Adaptive Dynamic Programming Control #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2511.06628
openalex publication_date 2025/11/10 · openalex created_date 2025/11/12 · openalex updated_date 2026/07/28
This paper is concerned with stochastic impulse control problems in which the running cost changes depending on the impulse control. Because of such a dependence, it brings several difficulties when the usual dynamic programming principle is to be used. The corresponding Hamilton-Jacobi-Bellman (HJB) equation (a quasi-variational inequality) is derived, which contains a parameter. The value function is a unique viscosity solution to this HJB equation by a classical argument. Further, inspired by the derivation of the Pontryagin type maximum principle for stochastic optimal controls with a non-convex control domain, we have established the maximum principle for our stochastic optimal impulse controls, allowing perturbations in optimal impulse moments.