{"title":"使用双时间尺度马尔可夫链的均值场优化切换的粘度解决方案","authors":"","doi":"10.1016/j.sysconle.2024.105895","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we consider the mean field optimal switching problem with a Markov chain under viscosity solution notion. Based on the conditional distribution of the Markov chain, the value function and corresponding dynamic programming principle are established. We prove that the value function is the unique viscosity solution of the variational inequality on Wasserstein space. In particular, we consider a two-time-scale Markov chain and derive the convergence of the limit system. As an application of theoretical results, an innovative example concerning the stock trading problem in a regime switching market is solved.</p></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":null,"pages":null},"PeriodicalIF":2.1000,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Viscosity solutions for mean field optimal switching with a two-time-scale Markov chain\",\"authors\":\"\",\"doi\":\"10.1016/j.sysconle.2024.105895\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we consider the mean field optimal switching problem with a Markov chain under viscosity solution notion. Based on the conditional distribution of the Markov chain, the value function and corresponding dynamic programming principle are established. We prove that the value function is the unique viscosity solution of the variational inequality on Wasserstein space. In particular, we consider a two-time-scale Markov chain and derive the convergence of the limit system. As an application of theoretical results, an innovative example concerning the stock trading problem in a regime switching market is solved.</p></div>\",\"PeriodicalId\":49450,\"journal\":{\"name\":\"Systems & Control Letters\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-08-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Systems & Control Letters\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S016769112400183X\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Systems & Control Letters","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S016769112400183X","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
Viscosity solutions for mean field optimal switching with a two-time-scale Markov chain
In this paper, we consider the mean field optimal switching problem with a Markov chain under viscosity solution notion. Based on the conditional distribution of the Markov chain, the value function and corresponding dynamic programming principle are established. We prove that the value function is the unique viscosity solution of the variational inequality on Wasserstein space. In particular, we consider a two-time-scale Markov chain and derive the convergence of the limit system. As an application of theoretical results, an innovative example concerning the stock trading problem in a regime switching market is solved.
期刊介绍:
Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.