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 creating a mathematical model of mortality, the importance, and the application of mortality tables, followed by the mathematical evolution of mortality models. It ends with the most recent model formulation – the stochastic mortality model. Next, the second section introduces parametric joint mortality models for coupled lives. It covers both the deterministic and stochastic model settings. Joint mortality models for coupled lives have great potential in the insurance industry for pricing joint and last survivor life insurance and annuity products (including pension products). As shown in previous studies, health condition and the expected life length of an individual can be significantly impacted by his or her significant partner, so consideration of bivariate mortality models can have significant practical importance. The third section summarizes nonparametric mortality models, for both individual and coupled lives. Compared with parametric models, the nonparametric ones are free of distributional assumptions and accordingly have a wider and more robust applications when understanding and parametrically modeling the true mortality distribution is not the focus of the study (e.g., when the focus is on studying the effects of covariates on mortality progression rather than mortality itself). Finally, in the fourth section, longevity risk and longevity risk models are introduced. These models are different from the mathematical models in previous sections in that these longevity risk models describe the changes of life expectancy between generations of individuals taking into consideration the cohort effects of people born in different years. These models have a great potential in solving longevity risk problems such as those occur in individual financial planning, institutional portfolio management, social security and medical insurance at a country level.