{"title":"Linear predictor of the discounted renewal aggregate claims with dependent inter-occurrence times","authors":"Franck Adékambi","doi":"10.4314/SAAJ.V18I1.2","DOIUrl":null,"url":null,"abstract":"In this paper we derive the first two moments and a linear predictor of the compound discounted renewal aggregate claims when taking into account dependence within the inter-occurrence times. Using specific mixtures of exponential distributions to define the dependence structure between the inter-occurrence times, we compare the accuracy of the proposed linear predictor to the simulated value of that sum.Keywords: Discounted compound renewal aggregate sums; moments; Archimedean copula; random interest rate; linear predictor","PeriodicalId":40732,"journal":{"name":"South African Actuarial Journal","volume":null,"pages":null},"PeriodicalIF":0.1000,"publicationDate":"2018-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"South African Actuarial Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4314/SAAJ.V18I1.2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
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Abstract
In this paper we derive the first two moments and a linear predictor of the compound discounted renewal aggregate claims when taking into account dependence within the inter-occurrence times. Using specific mixtures of exponential distributions to define the dependence structure between the inter-occurrence times, we compare the accuracy of the proposed linear predictor to the simulated value of that sum.Keywords: Discounted compound renewal aggregate sums; moments; Archimedean copula; random interest rate; linear predictor
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