Actuarial (Mathematical) Modeling of Mortality and Survival Curves

This chapter reviews the history, development, and application of mathematical mortality models. It consists of four sections. The first section focuses on parametric mortality models for single individuals. It starts with the innovation involved in creat

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Contents Introduction to the Development and History of Mathematical Models of Mortality . . . . . . . . Life Insurance Before the Invention of the Mortality Table . . . . . . . . . . . . . . . . . . . . . . . . . . Importance of Having a Mortality Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Innovation of Mortality Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . De Moivre and the First Creation of a Mathematical Law of Mortality . . . . . . . . . . . . . . . . . Gompertz and Makeham Laws of Mortality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Parametric Mortality Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stochastic Mortality Model for Individual Mortality Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . Joint Life Mortality Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Why Do We Need Joint Life Mortality Models? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Copula Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A New Stochastic Mortality Model for Joint Lives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nonparametric Estimation of the Mortality Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . One-Sample Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Joint Mortality Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mortality Modeling with Cohort Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Increasing in Human’s Life Expectancy and Longevity Risk . . . . . . . . . . . . . . . . . . . . . . . . . Lee-Carter Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Extensions of Lee-Carter Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mitchell et al. (2013)’s Extension of the Mortality Model . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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P. L. Brockett () Department of Information, Risk and Operations Management, University of Texas at Austin, Austin, TX, USA e-mail: [email protected] Y. Zhang Department of Management and Information Systems, Wayne State University, Detroit, MI, USA e-mail: [email protected] © Springer Nature Switzerland AG 2019 B. Sriraman (ed.), Handbook of the Mathematics of the Arts and Sciences, https://doi.org/10.1007/978-3-319-70658-0_69-1

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