{"title":"A note on portfolios of averages of lognormal variables","authors":"Phelim Boyle , Ruihong Jiang","doi":"10.1016/j.insmatheco.2023.06.001","DOIUrl":null,"url":null,"abstract":"<div><p>This paper establishes conditions under which a portfolio consisting of the averages of <em>K</em> blocks of lognormal variables converges to a <em>K</em>-dimensional lognormal variable as the number of variables in each block increases. The associated block covariance matrix has to have a special structure where the correlations and variances within the block submatrices are equal. We show why the variance homogeneity assumption plays a key role in the derivation.</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":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Insurance Mathematics & Economics","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167668723000562","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: 0
Abstract
This paper establishes conditions under which a portfolio consisting of the averages of K blocks of lognormal variables converges to a K-dimensional lognormal variable as the number of variables in each block increases. The associated block covariance matrix has to have a special structure where the correlations and variances within the block submatrices are equal. We show why the variance homogeneity assumption plays a key role in the derivation.
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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