Extreme Risk Analysis of Personal Insurance Claim Based on Block Maxima Method

Abstract

Recent years, the portion of personal insurance, including life insurance, health insurance and accident insurance, were getting larger and larger as the development of insurance market. Besides, the extreme risk of claims always exists in personal insurance. The domestic and foreign personal insurance practices have confirmed that mastery the extreme risk of claims can help insurance company pricing insurance products accurately. Therefore, the paper focused on quantifying the extreme risk of claims in personal insurance. Firstly, the principles of VaR (Value at Risk), extreme value theory, and Block Maxima Method (BM model) were sorted out, and then calculated VaR by theoretically derived. Furthermore, claim amounts of personal insurance in Beijing, Shanghai, Shaanxi Province, Henan Province, Inner Mongolia and Hainan province of China during 2005-2014 were chosen as samples. According to statistical analysis, the claim amounts datum with a same character of sharp peak and fat tail were filtered out, which contained accident insurance in Beijing, Shaanxi Province, Henan Province, Inner Mongolia, and Hainan Province as well as health insurance in Shanghai and Inner Mongolia. Lastly, the different time series of claims data were modeled by GEV distribution respectively, obtained the shape parameter, the position parameter, and the scale parameter, and then measured the extreme risk of each claims data based on BM model to get VaR of corresponding claims. The results show that the extreme risk of claims is more likely to arise in personal accident injury insurance, which exist in most regions. Since the occurrence of accident insurance does not conform to law of large numbers, its risk of claims is difficult to control. However, the extreme claim risk in health insurance has a relatively lower probability, whereas its claim VaR tends to be higher than that of personal accident injury insurance in extreme cases. Therefore, health insurance should be the focus of risk management in insurance company.