• 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.

• 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.

• Korean Journal of Medicinal Crop Science
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• v.12 no.6
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• pp.483-489
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• 2004

Monthly changes of underground growth and ethanol extract content was investigated from April to September in Korean ginseng of 4, 5 and 6 year-old. Taproot's length was repeatedly reduced and recovered without increasing by growth duration, while it's diameter was gradually increased until September of harvest time. Top weight reached to the peak on July, and decreased gradually until harvest time. Root weight of 4, 5 and 6-year-old ginseng was decreased on May, but increased gradually until harvest time except 6-year-old ginseng decreased after July. Relative growth rate (RGR) of root per plant was low on May and August, but high on June, July, and September in 4, 5 and 6 year-old ginseng. RGR of 4 and 5-year-old ginseng in each lateral and fine root showed distinct changes by month, while those showed little seasonal changes in 6 year-old ginseng. Ratio of root above 60g on september was 23%, 60% and 69%, respectively, among 4, 5 and 6 year-old ginseng. Moisture content of root was gradually decreased until september without significant difference from July to september in 4, 5 and 6 year-old ginseng, and its descending order on september was 4, 5 and 6 year-old ginseng. Hardness of taproot was decreased on May, but increased until september in 4 and 5 year-old ginseng, while that of 6 year-old ginseng was gradually decreased from August to september. Extract content of 4, 5 and 6 year-old ginseng in taproot and lateral root was distinctly decreased from March to June, but gradually increased until September. Although extract content of March and May in 4 year-old ginseng on showed higher than that of 5 and 6 year-old ginseng, it of September didn't show significant difference among 4, 5 and 6 year-old ginseng.