A Study on Modeling of Lifetime with Right-Truncated Composite Lognormal-Pareto Distribution: Actuarial Premium Calculations

Abstract

The modeling of lifetime is important to compute actuarial quantities such as the premium on insurance and annuity products. De Moivre, Gompertz, and Makeham are laws of mortality frequently used in lifetime modeling. Composite distributions have also been used to model lifetime, recently. However, there are not many actuarial applications of these models in the literature. Therefore, the main aim of the study is to perform a case study that gives a comparison of marginal and composite models on premiums. For this purpose, firstly, it is aimed to achieve a new mortality function for a lifetime using composite distribution. The second aim is to analytically compute premiums for whole life and term life insurance products. Here, it is assumed that lifetime distribution is modeled with lognormal, Type 2 Pareto (Pareto) and composite lognormal-Pareto. Firstly, the right truncated distributions of the models were obtained under the consideration that the last age of death was 100. Afterwards, the survival and mortality functions were inferenced using Mathematica 10.2 for the right truncated models. Finally, premium coefficients were analytically presented for whole life and term life insurances in single and joint life statuses. The results show that there are significantly differences in these premium coefficients. It has been observed that the premium coefficients for the term life insurance were higher than the premium coefficients for whole life insurance. In addition, the premium coefficients of the insurances issued for the joint life were smaller than the premium coefficients for the single life.

Keywords

• Composite lifetime
• Truncated distributions
• Mortality-survival
• Insurance premiums
• Single-joint life

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