A Study on Joint Life Insurance under a Common Shock Environment

Abstract

In this paper, we model the interdependent lifetime distribution considering a common shock environment experienced by couples. Then we analyze the premium and risk of joint life insurance and joint life annuity based on the proposed model. In addition, we will carry out the profit and loss analysis, and the risk analysis. They will also be compared with the existing model obtained under the assumption that the life times of the couples are independent. In the analysis, we assume that the couples are subject to heterogeneous shock environment. First, we briefly review the general method of calculating premiums and risks in whole life insurance and whole life annuity. Then we propose a dependent lifetime distribution of the couple sharing a common shock environment. In addition, we compare the proposed lifetime distribution and the lifetime distribution obtained under the assumption that times of the couple are independent. Based on these results, we examine the premium and risk of joint life insurance and joint life annuity, and examine the changes in premium and risk according to the contractor’s age and the common shock environment. We then examine the difference in premiums between the case where the actual life times are dependent and the case where the independence is assumed, and we find out where the difference comes from. Finally, the conclusions of this study are presented.;본 논문에서는 부부가 경험하는 common shock 요인을 고려하여 상호 의존적인 수명 분포를 모형화하고, 제안된 모형에 기초하여 연생보험과 연생연금의 보험료와 리스크를 분석하고자 한다. 또한, 부부의 수명이 독립적이라고 가정한 기존 모형과의 비교 분석을 수행하고자 하며, 보험계약자의 나이와 common shock 요인에 따른 보험료와 리스크의 변화 양상을 살펴보고자 한다. 이 때 common shock 요인에 의한 영향의 정도가 각 부부마다 다를 수 있다는 것을 고려하여 shock의 rate는 확률 변수로 정의하고 분석하고자 한다. 본 논문은 변수로 정의한 common shock 요인과 부부의 의존적인 수명분포를 고려하여 보다 현실성을 반영한 모형을 가정한 보험료와 리스크를 구할 수 있다는 점에서 의의가 있다.