{"title":"Utility Maximization of the Exponential Lévy Switching Models","authors":"Y. Dong, L. Vostrikova","doi":"10.1137/s0040585x97t991799","DOIUrl":null,"url":null,"abstract":"Theory of Probability &Its Applications, Volume 69, Issue 1, Page 127-149, May 2024. <br/> This article is devoted to maximization of HARA (hyperbolic absolute risk aversion) utilities of the exponential Lévy switching processes on a finite time interval via the dual method. The description of all $f$-divergence minimal martingale measures and the expression of their Radon--Nikodým densities involving the Hellinger and Kulback--Leibler processes are given. The optimal strategies in progressively enlarged filtration for the maximization of HARA utilities as well as the values of the corresponding maximal expected utilities are derived. As an example, the Brownian switching model is presented with financial interpretations of the results via the value process.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"20 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory of Probability and its Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/s0040585x97t991799","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
Theory of Probability &Its Applications, Volume 69, Issue 1, Page 127-149, May 2024. This article is devoted to maximization of HARA (hyperbolic absolute risk aversion) utilities of the exponential Lévy switching processes on a finite time interval via the dual method. The description of all $f$-divergence minimal martingale measures and the expression of their Radon--Nikodým densities involving the Hellinger and Kulback--Leibler processes are given. The optimal strategies in progressively enlarged filtration for the maximization of HARA utilities as well as the values of the corresponding maximal expected utilities are derived. As an example, the Brownian switching model is presented with financial interpretations of the results via the value process.
期刊介绍:
Theory of Probability and Its Applications (TVP) accepts original articles and communications on the theory of probability, general problems of mathematical statistics, and applications of the theory of probability to natural science and technology. Articles of the latter type will be accepted only if the mathematical methods applied are essentially new.