Stochastic Optimal Impulse Controls with Changing Running Costs

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autori principali: Cao, Yuchen, Yong, Jiongmin
Natura: Preprint
Pubblicazione: 2025
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866908640207699968
author Cao, Yuchen
Yong, Jiongmin
author_facet Cao, Yuchen
Yong, Jiongmin
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2511_06628
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Stochastic Optimal Impulse Controls with Changing Running Costs
Cao, Yuchen
Yong, Jiongmin
Optimization and Control
93E20, 93C27, 49L25, 49N25
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.
title Stochastic Optimal Impulse Controls with Changing Running Costs
topic Optimization and Control
93E20, 93C27, 49L25, 49N25
url https://arxiv.org/abs/2511.06628