EVT and Its Application to Pricing of Catastrophe (Typhoon) Reinsurance

Hu Yue; Zhang Li; Shen Li-jie; Gao Li-ya

doi:doi:10.11648/j.ajam.20160402.16

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EVT and Its Application to Pricing of Catastrophe (Typhoon) Reinsurance

Hu Yue, Zhang Li, Shen Li-jie, Gao Li-ya

Published in American Journal of Applied Mathematics (Volume 4, Issue 2)

Received: 10 April 2016 Published: 11 April 2016

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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.

Published in	American Journal of Applied Mathematics (Volume 4, Issue 2)
DOI	10.11648/j.ajam.20160402.16
Page(s)	105-109
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Extreme Value Theory, POT, Reinsurance, Pure Premium

References

[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.

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APA Style

Hu Yue, Zhang Li, Shen Li-jie, Gao Li-ya. (2016). EVT and Its Application to Pricing of Catastrophe (Typhoon) Reinsurance. American Journal of Applied Mathematics, 4(2), 105-109. https://doi.org/10.11648/j.ajam.20160402.16

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ACS Style

Hu Yue; Zhang Li; Shen Li-jie; Gao Li-ya. EVT and Its Application to Pricing of Catastrophe (Typhoon) Reinsurance. Am. J. Appl. Math. 2016, 4(2), 105-109. doi: 10.11648/j.ajam.20160402.16

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AMA Style

Hu Yue, Zhang Li, Shen Li-jie, Gao Li-ya. EVT and Its Application to Pricing of Catastrophe (Typhoon) Reinsurance. Am J Appl Math. 2016;4(2):105-109. doi: 10.11648/j.ajam.20160402.16

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@article{10.11648/j.ajam.20160402.16,
  author = {Hu Yue and Zhang Li and Shen Li-jie and Gao Li-ya},
  title = {EVT and Its Application to Pricing of Catastrophe (Typhoon) Reinsurance},
  journal = {American Journal of Applied Mathematics},
  volume = {4},
  number = {2},
  pages = {105-109},
  doi = {10.11648/j.ajam.20160402.16},
  url = {https://doi.org/10.11648/j.ajam.20160402.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160402.16},
  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.},
 year = {2016}
}

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TY  - JOUR
T1  - EVT and Its Application to Pricing of Catastrophe (Typhoon) Reinsurance
AU  - Hu Yue
AU  - Zhang Li
AU  - Shen Li-jie
AU  - Gao Li-ya
Y1  - 2016/04/11
PY  - 2016
N1  - https://doi.org/10.11648/j.ajam.20160402.16
DO  - 10.11648/j.ajam.20160402.16
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 105
EP  - 109
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20160402.16
AB  - 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.
VL  - 4
IS  - 2
ER  -

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Author Information

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

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APA Style

Hu Yue, Zhang Li, Shen Li-jie, Gao Li-ya. (2016). EVT and Its Application to Pricing of Catastrophe (Typhoon) Reinsurance. American Journal of Applied Mathematics, 4(2), 105-109. https://doi.org/10.11648/j.ajam.20160402.16

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ACS Style

Hu Yue; Zhang Li; Shen Li-jie; Gao Li-ya. EVT and Its Application to Pricing of Catastrophe (Typhoon) Reinsurance. Am. J. Appl. Math. 2016, 4(2), 105-109. doi: 10.11648/j.ajam.20160402.16

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AMA Style

Hu Yue, Zhang Li, Shen Li-jie, Gao Li-ya. EVT and Its Application to Pricing of Catastrophe (Typhoon) Reinsurance. Am J Appl Math. 2016;4(2):105-109. doi: 10.11648/j.ajam.20160402.16

Copy | Download

@article{10.11648/j.ajam.20160402.16,
  author = {Hu Yue and Zhang Li and Shen Li-jie and Gao Li-ya},
  title = {EVT and Its Application to Pricing of Catastrophe (Typhoon) Reinsurance},
  journal = {American Journal of Applied Mathematics},
  volume = {4},
  number = {2},
  pages = {105-109},
  doi = {10.11648/j.ajam.20160402.16},
  url = {https://doi.org/10.11648/j.ajam.20160402.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160402.16},
  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.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - EVT and Its Application to Pricing of Catastrophe (Typhoon) Reinsurance
AU  - Hu Yue
AU  - Zhang Li
AU  - Shen Li-jie
AU  - Gao Li-ya
Y1  - 2016/04/11
PY  - 2016
N1  - https://doi.org/10.11648/j.ajam.20160402.16
DO  - 10.11648/j.ajam.20160402.16
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 105
EP  - 109
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20160402.16
AB  - 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.
VL  - 4
IS  - 2
ER  -

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