{"title":"Diversification quotients based on VaR and ES","authors":"Xia Han , Liyuan Lin , Ruodu Wang","doi":"10.1016/j.insmatheco.2023.08.006","DOIUrl":null,"url":null,"abstract":"<div><p>The diversification quotient (DQ) is recently introduced for quantifying the degree of diversification of a stochastic portfolio model. It has an axiomatic foundation and can be defined through a parametric class of risk measures. Since the Value-at-Risk (VaR) and the Expected Shortfall (ES) are the most prominent risk measures widely used in both banking and insurance, we investigate DQ constructed from VaR and ES in this paper. In particular, for the popular models of elliptical and multivariate regular varying (MRV) distributions, explicit formulas are available. The portfolio optimization problems for the elliptical and MRV models are also studied. Our results further reveal favorable features of DQ, both theoretically and practically, compared to traditional diversification indices based on a single risk measure.</p></div>","PeriodicalId":54974,"journal":{"name":"Insurance Mathematics & Economics","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Insurance Mathematics & Economics","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167668723000781","RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ECONOMICS","Score":null,"Total":0}
引用次数: 1
Abstract
The diversification quotient (DQ) is recently introduced for quantifying the degree of diversification of a stochastic portfolio model. It has an axiomatic foundation and can be defined through a parametric class of risk measures. Since the Value-at-Risk (VaR) and the Expected Shortfall (ES) are the most prominent risk measures widely used in both banking and insurance, we investigate DQ constructed from VaR and ES in this paper. In particular, for the popular models of elliptical and multivariate regular varying (MRV) distributions, explicit formulas are available. The portfolio optimization problems for the elliptical and MRV models are also studied. Our results further reveal favorable features of DQ, both theoretically and practically, compared to traditional diversification indices based on a single risk measure.
期刊介绍：
Insurance: Mathematics and Economics publishes leading research spanning all fields of actuarial science research. It appears six times per year and is the largest journal in actuarial science research around the world.
Insurance: Mathematics and Economics is an international academic journal that aims to strengthen the communication between individuals and groups who develop and apply research results in actuarial science. The journal feels a particular obligation to facilitate closer cooperation between those who conduct research in insurance mathematics and quantitative insurance economics, and practicing actuaries who are interested in the implementation of the results. To this purpose, Insurance: Mathematics and Economics publishes high-quality articles of broad international interest, concerned with either the theory of insurance mathematics and quantitative insurance economics or the inventive application of it, including empirical or experimental results. Articles that combine several of these aspects are particularly considered.
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