• 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.

• 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.31 no.1
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• pp.77-96
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• 2018

A reverse mortgage provides a pension until the death for the insured or last survivor. Long-term risk management is important to estimate the contractual period of a reverse mortgage. It is also necessary to study prediction methods of mortality rates that appropriately reflect the improvement trend of the mortality rate since the extension of the life expectancy, which is the main cause of aging, can have a serious impact on the pension financial soundness. In this study, the Lee-Carter (LC) model reflects the improvement in mortality rates; in addition, multiple life model are also applied to a reverse mortgage. The mortality prediction method by the traditional LC model has shown a dramatic improvement in the mortality rate; therefore, this study suggests mortality projection based on the projection of the skewness for the mortality that has been applied to appropriately reflect the improvement trend of the mortality rate. This paper calculates monthly payments using future mortality rates based on the projection of the skewness of the mortality. As a result, the mortality rates based on this method less reflect the mortality improvement effect than the mortality rates based on a traditional LC model and a larger pension amount is calculated. In conclusion, this method is useful to forecast future mortality trend results in a significant reduction of longevity risk. It can also be used as a risk management method to pay appropriate monthly payments and prevent insufficient payment due to overpayment by the issuing institution and the guarantee institution of the reverse mortgage.