Volume 6, Issue 4, August 2018, Page: 192-199
Extreme Risk Analysis of Personal Insurance Claim Based on Block Maxima Method
Tian Yaqiong, Department of Economics, Central University of Finance and Economics, Beijing, China
Received: Jul. 31, 2018;       Accepted: Aug. 22, 2018;       Published: Sep. 21, 2018
DOI: 10.11648/j.ijefm.20180604.17      View  556      Downloads  73
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.
Personal Insurance, BM Model, GEV Distribution, Claim Amount, VaR
To cite this article
Tian Yaqiong, Extreme Risk Analysis of Personal Insurance Claim Based on Block Maxima Method, International Journal of Economics, Finance and Management Sciences. Vol. 6, No. 4, 2018, pp. 192-199. doi: 10.11648/j.ijefm.20180604.17
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Zhang Ruiwu. Risks and countermeasures of claim management in life insurance companies [J]. Shanghai Insurance, 2010, (2): 44-46.
Liu Yuhuan, Fang Rongjun. Analysis on challenge to life insurance brought by new “Insurance Law” and countermeasures [J]. Journal of Financial Development Reasearch, 2010, (5): 79-82.
Zhang Yi, Wu Haibo. Health insurance claims: Problems, roots and ways [J]. Journal of Finance and Economics, 2011, (1):83-85.
Yan Su, Fu Jiangtao. The VaR model and its application in risk management of life insurance companies [J].Insurance Studies, 2009, (2): 78-83.
Longin F. M. The asymptotic distribution of extreme stock market returns [J],Journal of business, 1996, 69(3): 383-408.
Alexander J. McNeil. Extreme value theory for risk managers [J]. Internal Modeling and CAD Ⅱ published by RISK Books, 1999, (5): 93-113.
Guillen M, Prieto F, Sarabia J M. Modelling losses and locating the tail with the Pareto Stable distribution [J]. Insurance: Math. Econ., 2011, 49(3): 454-461.
Xuan Haiyan, Bao Haiming, SHI Yongxia. Application of the pareto positive stable distribution in insurance claim [J]. Journal of Mathematics, 2015, 35(4): 889-897.
Zhao Zhihong, Li Xingxu. Fitting and actuarial research on extremely large loss in non-life insurance [J]. Journal of Applied Statistics and Management, 2010, 29(2):336-347.
Ren Jing, Zhang Jiesong. POT model and its application to simulate the catastrophe loss distribution and risk measrement [J]. Science-Technology and Management, 2015, 31(4):7-13.
Hao Junhang, Cui Yujie. Research on catastrophe risk measurement and insurance model based on POT model——Taking earth quake risk as an example [J]. Journal of Applied Statistics and Management, 2016, 35(1): 132-141.
Qian Yiping, Lin Xiang, Chen Zhiya. Application of BMM model in operation risk measurement of commercial banks [J]. Statistics & Decision, 2010, (7): 68-71.
Hua Yongjun, Gao Yuandong, Zhang Zongyi. The research of BMM model for stationary sequence and extreme risk of Shenzhen and Shanghai stock market, Mathematics in Practice and Theory. 2011, 41(18): 68-71.
Liu Fei, Zheng Xiaoya. Catastrophic risk measurement and insurance model study based on POT model——A case of seismic risk [J]. Journal of China University of Petroleum (Edition of Social Sciences), 2015, 29(2): 7-13.
Li Zhen, Lu Wenyuan. Research on financial extreme risk based on BMM model and empirical analysis. [J]. Science Technology and Industry, 2017, (11): 148-152.
Yuan Xucheng. Enhancing the soft power of the insurance industry [J]. China Finance, 2018, (4): 52-54.
Yu Huan, Zhou Shihan, Hu Yuting. Research on risk measurement of High-value Critical Care Medical insurance claims based on POT model [J]. Economic & Trade, 2018, (12): 54-55.
Shang Weiping, Zhang Jianwei, Dai Yu. Comparative study and empirical analysis of VaR and CVaR Based on extreme value theory [J]. Financial Perspectives Journal, 2017, (10): 90-98.
Xu Qifa, Jiang Cuixia. R Programming with applications to financial quantitative analysis [M]. Tsinghua University Press, 2015.
Zhuo Zhi, Sun Zhengcheng. On whether health insurance can improve business performance of insurance companies——the business impetus of domestic commercial health insurance [J]. Finance & Economics, 2015, (11): 34-44.
Wang Jun, Gao Feng, Leng Huiqing. Test of moral hazard in health insurance market [J]. Management World, 2010, (6): 50-55.
Zhang Miaoli, Lan Shaoqing, Luo Qian. Research on the regional development status of health insurance in China from 2006 to 2015 [J]. Chinese Health Economics, 2018, (4): 33-36.
Wang Xiangnan, Bian Wenlong. Market structure and level of compensation: the health insurance in China from 2004 to 2014 [J]. Modern Economic Science, 2016, (5):1-11+124.
S. A. Abu Bakar, N. A. Hamzah, M. Maghsoudi. Modeling loss data using composite models [M]. 2015.
L Zheng, K Ismail, X Meng. Freeway safety estimation using extreme value theory approaches: A comparative study [J]. Accident Analysis & Prevention, 2013, (62): 32-41.
A Ferreira, L De Haan. On the block maxima method in extreme value theory: PWM estimators [J],The Annals of Statistics, 2015, 43(1): 276-298.
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