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Volume 4, Issue 2, April 2016, Page: 105-109
EVT and Its Application to Pricing of Catastrophe (Typhoon) Reinsurance
Hu Yue, Department of Mathematics and Information Science, Zhejiang University of Science and Technology, Hangzhou, P.R. China
Zhang Li, Department of Mathematics and Information Science, Zhejiang University of Science and Technology, Hangzhou, P.R. China
Shen Li-jie, Department of Mathematics and Information Science, Zhejiang University of Science and Technology, Hangzhou, P.R. China
Gao Li-ya, Department of Mathematics and Information Science, Zhejiang University of Science and Technology, Hangzhou, P.R. China
Received: Apr. 10, 2016;       Published: Apr. 11, 2016
Abstract
Extreme value theory is a branch of the theory of order statistics and it is a statistical study of extreme events disciplined approach. There is often extreme values in catastrophe losses, the use of traditional methods of statistical laws describe the amount of catastrophe losses would ignore the existence of extreme data. In this paper, we consider the premium of excess-of-loss reinsurance policies with different attachment points based on the idea of layered pricing using extreme value model, and we fit POT model to the typhoon loss date of Zhejiang Province to determine the pure premium of typhoon in the empirical analysis.
Keywords
Extreme Value Theory, POT, Reinsurance, Pure Premium
Hu Yue, Zhang Li, Shen Li-jie, Gao Li-ya, EVT and Its Application to Pricing of Catastrophe (Typhoon) Reinsurance, American Journal of Applied Mathematics. Vol. 4, No. 2, 2016, pp. 105-109. doi: 10.11648/j.ajam.20160402.16
Reference
[1]
Mcneil, A. J. Extreme value theory for risk managers [M]. Internal Modeling CaDII, Risk Books, 1999, 93-113.
[2]
Fisher R. Tippett L. Limiting forms of the frequency distribution of the large or smallest member of a sample [J]. Procedings of the Cambridge Philosophical Society, 1928 (24).
[3]
Gumbel E. Statistics of extreme [M]. New York: Columbia University Press. 1958.
[4]
SHI Dao-ji, Practical extreme value statistical method, Tianjin: Tianjin science and Technology Press [M], 2006.
[5]
Tawn, J, A. Bivariate Extreme Value Theory-Models and Estimation [J]. Biometrika, 1988.
[6]
ZHAO Zhi-hong, LI Xing-xu, Fitting and Actuarial Research on Extremely Large Loss in Non-life Insurance [J], Application of Statistics and Management, 2010, 29(3): 336-347.
[7]
Song Jia-shan, Li yong and Peng cheng, Improvement of Hill estimation method for threshold selection in extreme value theory [J], Application of University of Science & Technology China, 2008, (9): 1104-1108.
[8]
OUYANG Zi-sheng, Extreme Quantile Estimation for Heavy-tailed Distribution and A study of Extremal Risk Measurement[J], Application of Statistics and Management, 2008, 27(1): 70-75.
[9]
XIAO Hai-qing, MENG Sheng-wang, EVT and Its Application to Pricing of Catastrophe Reinsurance[J], Application of Statistics and Management, 2013,32(2): 1002-1566.
[10]
Jiang Zheng-fa and Huang xu-peng, An actuarial model of life insurance premiums based on Compound Poisson process [J]. Application of Statistics and decision making, 2014 (8): 57-59.
[11]
THE ALMANAC OF ZHEJIANG, THE ALMANAC OF TYPHOON.