{"title":"Portfolio Value-at-Risk Approximation for Geometric Brownian Motion","authors":"H. Kechejian, V. K. Ohanyan, V. G. Bardakhchyan","doi":"10.3103/s1068362324700067","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Value-at-risk (VaR) serves as a measure for assessing the risk associated with individual securities and portfolios. When calculating VaR for portfolios, the dimension of the covariance matrix increases as more securities are included. In this study, we present a solution to address the issue of dimensionality by directly computing the VaR of a portfolio using a single security, therefore requiring only one variance and one mean. Our results demonstrate that, under the assumption of Gaussian distribution, the deviation between the computed VaR and actual values is relatively small.</p>","PeriodicalId":54854,"journal":{"name":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3103/s1068362324700067","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Value-at-risk (VaR) serves as a measure for assessing the risk associated with individual securities and portfolios. When calculating VaR for portfolios, the dimension of the covariance matrix increases as more securities are included. In this study, we present a solution to address the issue of dimensionality by directly computing the VaR of a portfolio using a single security, therefore requiring only one variance and one mean. Our results demonstrate that, under the assumption of Gaussian distribution, the deviation between the computed VaR and actual values is relatively small.
期刊介绍：
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) is an outlet for research stemming from the widely acclaimed Armenian school of theory of functions, this journal today continues the traditions of that school in the area of general analysis. A very prolific group of mathematicians in Yerevan contribute to this leading mathematics journal in the following fields: real and complex analysis; approximations; boundary value problems; integral and stochastic geometry; differential equations; probability; integral equations; algebra.
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