{"title":"On Numerical Problems in Computing Life Annuities Based on the Makeham–Beard Law","authors":"Fredy Castellares, Artur J. Lemonte","doi":"10.1515/ms-2023-0096","DOIUrl":null,"url":null,"abstract":"ABSTRACT Analytic expressions for the single and joint life annuities based on the Makeham–Beard mortality law have been derived recently in the literature, which depend on special mathematical functions such as hypergeometric functions. We verify that the arguments of the hypergeometric functions in the analytic expressions for the single and joint life annuities may assume values very close to unity (boundary of the convergence radius), and so numerical problems may arise when using them in practice. We provide, therefore, alternative analytic expressions for the single and joint life annuities where the arguments of the hypergeometric functions in the new analytic expressions do not assume values close to one.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica Slovaca","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/ms-2023-0096","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
ABSTRACT Analytic expressions for the single and joint life annuities based on the Makeham–Beard mortality law have been derived recently in the literature, which depend on special mathematical functions such as hypergeometric functions. We verify that the arguments of the hypergeometric functions in the analytic expressions for the single and joint life annuities may assume values very close to unity (boundary of the convergence radius), and so numerical problems may arise when using them in practice. We provide, therefore, alternative analytic expressions for the single and joint life annuities where the arguments of the hypergeometric functions in the new analytic expressions do not assume values close to one.
期刊介绍：
Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process. Its reputation was approved by many outstanding mathematicians who already contributed to Math. Slovaca. It makes bridges among mathematics, physics, soft computing, cryptography, biology, economy, measuring, etc. The Journal publishes original articles with complete proofs. Besides short notes the journal publishes also surveys as well as some issues are focusing on a theme of current interest.
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