응용통계연구 (The Korean Journal of Applied Statistics)

  • 제27권7호
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  • Pages.1097-1114
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  • 2014
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  • 1225-066X(pISSN)
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  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
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코퓰라와 커먼-쇽을 이용한 연생상품의 분석

Analysis of Multiple Life Insurance using Copula and Common Shock

  • 김도영 (성균관대학교 보험계리학과) ;
  • 이삭 (성균관대학교 보험계리학과) ;
  • 이항석 (성균관대학교 보험계리학과)
  • Kim, Doyoung (Department of Actuarial Science, Sungkyunkwan University) ;
  • Lee, Issac (Department of Actuarial Science, Sungkyunkwan University) ;
  • Lee, Hangsuck (Department of Actuarial Science, Sungkyunkwan University)
  • 투고 : 2014.09.14
  • 심사 : 2014.12.04
  • 발행 : 2014.12.31
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초록

연생보험은 보험가입자 2인의 생사여부에 따라 보험금을 지급하는 보험상품이다. 보험실무에서는 연생보험 가입자들의 장래생존기간을 독립으로 가정하고 보험료를 산출한다. 그러나 보험가입자들 사이에 존재하는 상관성을 고려할 때 이는 합리적이지 않다. 또한 보험가입자들의 생존분포와 독립적인 커먼-쇽(common shock)을 연생보험에 반영하면 다양한 지급조건을 설정할 수 있는데 이에 대한 충분한 고려가 이루어지지 않고 있다. 본 논문에서는 커먼-쇽(common shock)을 연생보험에 적용하고, 코퓰라(copula)를 이용하여 가입자들의 장래생존기간 간에 존재하는 상관성을 반영한 후 분석을 수행한다. 또한 연생보험가입자에 대한 확률변수를 추가적으로 고려하여 기존의 연생모형에서 다루지 못했던 새로운 상품을 설계하고 시뮬레이션을 통해 보험료를 계산한다. 그리고 그 결과를 바탕으로 본 논문에서 제시한 모형이 연생상품에 다양하게 적용 가능함을 논하고자 한다.

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.

키워드

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