新風險指標Riskiness在保險費訂價上的應用

Abstract

Robert J. Aumann與Roberto Serrano於2008年發表於Journal of Political Economy的新風險指標－Riskiness，其具有比以往常用的風險指標如變異數、標準差或風險值(VaR)更好的經濟和數學性質，因為其只考慮賭局本身報酬之分配，而獨立於投資者之風險偏好為一客觀指標，此外，其還服從一階隨機單調與二階隨機單調，且具有強調損失面的特性，在實務使用上相當符合需求且便利。 本文即將此風險指標－Riskiness，運用在保險公司之保單設計上，即把保險公司收取保費，並在保戶出險時依照合約內容給付保險金視為一個賭局，研究保險公司應如何搭配目前常使用的自負額、共保比例與給付上限等方式來設計保險合約，使保險公司能在達到一定的保費收入目標下，又能使其承擔的風險最小。

The new risk index proposed in Journal of Political Economy by Robert J. Aumann and Roberto Serrano in 2008－Riskiness, which has better economic and mathematical properties than commonly used indicators of risk such as variance, standard deviation or value at risk (VaR) because it only takes the gamble’s return into account and be independent from the risk preference of investors. Thus we can measure the risk objectively through it. In addition, the character of monotonicity with respect to stochastic dominance and putting more emphasis on loss bring more convenience in practical use. In this paper, I applied the risk index Riskiness to insurance contract design to see how an insurance company can minimize its risk under fixed premium income.