{"title":"Existence of relaxed stochastic optimal control for G-SDEs with controlled jumps","authors":"A. Redjil, H. B. Gherbal, O. Kebiri","doi":"10.1080/07362994.2021.1991809","DOIUrl":null,"url":null,"abstract":"Abstract In this article, we study the relaxed control problem where the admissible controls are measure-valued processes and the state variable is governed by a G-stochastic differential equation (SDEs) driven by a relaxed Poisson measure where the compensator is a product measure. The control variable appears in the drift and in the jump term. We prove that every solution of our SDE associated to a relaxed control can be written as a limit of a sequence of solutions of SDEs associated to strict controls (stability results). In the end, we show the existence of our relaxed control.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"41 1","pages":"115 - 133"},"PeriodicalIF":0.8000,"publicationDate":"2021-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastic Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/07362994.2021.1991809","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 1
Abstract
Abstract In this article, we study the relaxed control problem where the admissible controls are measure-valued processes and the state variable is governed by a G-stochastic differential equation (SDEs) driven by a relaxed Poisson measure where the compensator is a product measure. The control variable appears in the drift and in the jump term. We prove that every solution of our SDE associated to a relaxed control can be written as a limit of a sequence of solutions of SDEs associated to strict controls (stability results). In the end, we show the existence of our relaxed control.
期刊介绍：
Stochastic Analysis and Applications presents the latest innovations in the field of stochastic theory and its practical applications, as well as the full range of related approaches to analyzing systems under random excitation. In addition, it is the only publication that offers the broad, detailed coverage necessary for the interfield and intrafield fertilization of new concepts and ideas, providing the scientific community with a unique and highly useful service.
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