• The Korean Journal of Applied Statistics
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• v.27 no.7
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• pp.1097-1114
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• 2014

Multiple-life policies pay a benefit on the first death or the last death among the group of lives. In practice, the future lifetime random variable of policy holders has been considered to be independent, but it is more rational to take into account the correlations among the policy holders. In this paper, the Gaussian copula is applied to re ect the correlations among policy holders and then to diversify the common shock of the multiple life policies which follows an exponential distribution. Five case studies demonstrate its usefulness of using copula in calculating the premiums of the multiple-life policies including the common shock.

• Communications for Statistical Applications and Methods
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• v.18 no.6
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• pp.771-785
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• 2011

Most studies on the joint life insurance assume the lifetimes of insurers to be mutually independent; however, there have been various studies that illustrate the dependency of insurers' lifetimes. Subsequently, some approaches to model this type of dependency have been suggested. This paper proposes a joint dependent lifetime distribution for coupled lives under common environmental effect and applies the proposed model to the study of the joint life insurance. In addition, we investigate the effect of the false assumption of independent lifetimes when there exists dependency between the insurers' lifetimes assumed in this paper.

• The Korean Journal of Applied Statistics
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• v.26 no.3
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• pp.531-547
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• 2013

Multiple life models are useful in multiple life insurance and multiple life annuities when the payment times of benets in these insurance products are contingent on the future life times of at least two people. A reverse mortgage is an annuity whose monthly payments terminate at the death time of the last survivor; however, actuaries have used female life table to calculate monthly payments of a reverse mortgage. This approach may overestimate monthly payments. This paper suggests a last-survivor life table rather than a female life table to avoid the overestimation of monthly payments. Next, this paper derives the distribution of the future life time of last survivor, and calculates the expected life times of male, female and last survivor. This paper calculates principal limits and monthly payments in cases of male life table, female life table and last-survivor life table, respectively. Some numerical examples are discussed.

• Journal of the Korean Data and Information Science Society
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• v.26 no.4
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• pp.931-946
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• 2015

Many multiple life insurance products consider benefits that are contingent on the combined survival status of two lives. To value premiums of the insurance products accurately, we need to consider the impact of the survivorship of one life on another. To show a dependence relation between married couple, we calculate correlation coefficients by using married couples data from National Pension Service and the results show some positive dependence between them. Moreover, by analyzing the death after bereavement, we find a evidence that mortality rates increase after the death of a spouse and, in addition, that this phenomenon, the broken-heart syndrome, diminishes over time. The results of this study can support the method to calculate the premium of multiple life insurance reflecting more realistic joint mortality rates.