{"title":"Reserves in the multi-state health insurance model with stochastic interest of diffusion type","authors":"Franck Adékambi","doi":"10.4314/SAAJ.V15I0.5","DOIUrl":null,"url":null,"abstract":"In this paper, we consider the Markovian model for the actuarial modelling of health insurance policies modified by the inclusion of durational effects (the time elapsed since entering a given state) on the aggregate payment streams, where the force of interest is a diffusion process. We derive differential equations for the first moment of the present value of the aggregate amount of benefits. We also give two examples to illustrate our results.","PeriodicalId":40732,"journal":{"name":"South African Actuarial Journal","volume":"15 1","pages":"109-129"},"PeriodicalIF":0.1000,"publicationDate":"2015-01-01","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.V15I0.5","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 consider the Markovian model for the actuarial modelling of health insurance policies modified by the inclusion of durational effects (the time elapsed since entering a given state) on the aggregate payment streams, where the force of interest is a diffusion process. We derive differential equations for the first moment of the present value of the aggregate amount of benefits. We also give two examples to illustrate our results.
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