The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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A Study on the Determination of the Risk-Loaded Premium using Risk Measures in the Credibility Theory

신뢰도이론에서 위험측도를 이용한 할증보험료 결정에 대한 고찰

  • Kim, Hyun Tae (Department of Applied Statistics, Yonsei University) ;
  • Jeon, Yongho (Department of Applied Statistics, Yonsei University)
  • 김현태 (연세대학교 상경대학 응용통계학과) ;
  • 전용호 (연세대학교 상경대학 응용통계학과)
  • Received : 2013.10.23
  • Accepted : 2013.11.11
  • Published : 2014.02.28
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Abstract

The Bayes premium or the net premium in the credibility theory does not reflect the underlying tail risk. In this study we examine how the tail risk measures can be utilized in determining the risk premium. First, we show that the risk measures can not only provide the proper risk loading, but also allow the insurer to avoid the wrong decision made with the Bayesian premium alone. Second, it is illustrated that the rank of the tail thickness among different conditional loss distributions does not preserve for the corresponding predictive distributions, even if they share the identical prior variable. The implication of this result is that the risk loading for a contract should be based on the risk measure of the predictive loss distribution not the conditional one.

손해보험의 신뢰도이론에서 순보험료로 사용되는 베이즈보험료는 꼬리위험을 반영하지 못한다는 한계점이 있다. 본 논문에서는 꼬리위험측도를 이용하여 할증보험료를 결정하는데 있어 중요하다고 여겨지는 두 가지 주제를 다루었다. 첫째, 위험측도로부터 유도되는 안전할증은 내재된 담보의 위험을 보다 정확히 반영할 수 있으며, 동시에 베이즈보험료만을 사용할 경우 초래될 수 있는 잘못된 의사결정을 피할 수 있음을 보였다. 둘째, 동일한 사전분포가 주어지더라도 서로 다른 조건부손실분포의 꼬리위험 순위와 그에 상응하는 예측분포의 꼬리위험순위는 일반적으로 다를 수 있음을 모수적 모형에 기반하여 보였다. 따라서 안전할증은 조건부손실분포의 위험측도가 아니라 예측분포의 위험측도를 사용해야 함을 알 수 있다.

Keywords

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