{"ID":2843687,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.06628","arxiv_id":"2511.06628","title":"Stochastic Optimal Impulse Controls with Changing Running Costs","abstract":"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.","short_abstract":"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-...","url_abs":"https://arxiv.org/abs/2511.06628","url_pdf":"https://arxiv.org/pdf/2511.06628v1","authors":"[\"Yuchen Cao\",\"Jiongmin Yong\"]","published":"2025-11-10T02:15:34Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[\"Large Language Model\"]","has_code":false}