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

Tian Yaqiong

doi:doi:10.11648/j.ijefm.20180604.17

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

Tian Yaqiong

Published in International Journal of Economics, Finance and Management Sciences (Volume 6, Issue 4)

Received: 31 July 2018 Accepted: 22 August 2018 Published: 21 September 2018

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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.

Published in	International Journal of Economics, Finance and Management Sciences (Volume 6, Issue 4)
DOI	10.11648/j.ijefm.20180604.17
Page(s)	192-199
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), 2018. Published by Science Publishing Group

Keywords

Personal Insurance, BM Model, GEV Distribution, Claim Amount, VaR

References

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APA Style

Tian Yaqiong. (2018). Extreme Risk Analysis of Personal Insurance Claim Based on Block Maxima Method. International Journal of Economics, Finance and Management Sciences, 6(4), 192-199. https://doi.org/10.11648/j.ijefm.20180604.17

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ACS Style

Tian Yaqiong. Extreme Risk Analysis of Personal Insurance Claim Based on Block Maxima Method. Int. J. Econ. Finance Manag. Sci. 2018, 6(4), 192-199. doi: 10.11648/j.ijefm.20180604.17

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AMA Style

Tian Yaqiong. Extreme Risk Analysis of Personal Insurance Claim Based on Block Maxima Method. Int J Econ Finance Manag Sci. 2018;6(4):192-199. doi: 10.11648/j.ijefm.20180604.17

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@article{10.11648/j.ijefm.20180604.17,
  author = {Tian Yaqiong},
  title = {Extreme Risk Analysis of Personal Insurance Claim Based on Block Maxima Method},
  journal = {International Journal of Economics, Finance and Management Sciences},
  volume = {6},
  number = {4},
  pages = {192-199},
  doi = {10.11648/j.ijefm.20180604.17},
  url = {https://doi.org/10.11648/j.ijefm.20180604.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijefm.20180604.17},
  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.},
 year = {2018}
}

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TY  - JOUR
T1  - Extreme Risk Analysis of Personal Insurance Claim Based on Block Maxima Method
AU  - Tian Yaqiong
Y1  - 2018/09/21
PY  - 2018
N1  - https://doi.org/10.11648/j.ijefm.20180604.17
DO  - 10.11648/j.ijefm.20180604.17
T2  - International Journal of Economics, Finance and Management Sciences
JF  - International Journal of Economics, Finance and Management Sciences
JO  - International Journal of Economics, Finance and Management Sciences
SP  - 192
EP  - 199
PB  - Science Publishing Group
SN  - 2326-9561
UR  - https://doi.org/10.11648/j.ijefm.20180604.17
AB  - 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.
VL  - 6
IS  - 4
ER  -

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Author Information

Tian Yaqiong

Department of Economics, Central University of Finance and Economics, Beijing, China

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Plain Text BibTeX RIS

APA Style

Tian Yaqiong. (2018). Extreme Risk Analysis of Personal Insurance Claim Based on Block Maxima Method. International Journal of Economics, Finance and Management Sciences, 6(4), 192-199. https://doi.org/10.11648/j.ijefm.20180604.17

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ACS Style

Tian Yaqiong. Extreme Risk Analysis of Personal Insurance Claim Based on Block Maxima Method. Int. J. Econ. Finance Manag. Sci. 2018, 6(4), 192-199. doi: 10.11648/j.ijefm.20180604.17

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AMA Style

Tian Yaqiong. Extreme Risk Analysis of Personal Insurance Claim Based on Block Maxima Method. Int J Econ Finance Manag Sci. 2018;6(4):192-199. doi: 10.11648/j.ijefm.20180604.17

Copy | Download

@article{10.11648/j.ijefm.20180604.17,
  author = {Tian Yaqiong},
  title = {Extreme Risk Analysis of Personal Insurance Claim Based on Block Maxima Method},
  journal = {International Journal of Economics, Finance and Management Sciences},
  volume = {6},
  number = {4},
  pages = {192-199},
  doi = {10.11648/j.ijefm.20180604.17},
  url = {https://doi.org/10.11648/j.ijefm.20180604.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijefm.20180604.17},
  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.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Extreme Risk Analysis of Personal Insurance Claim Based on Block Maxima Method
AU  - Tian Yaqiong
Y1  - 2018/09/21
PY  - 2018
N1  - https://doi.org/10.11648/j.ijefm.20180604.17
DO  - 10.11648/j.ijefm.20180604.17
T2  - International Journal of Economics, Finance and Management Sciences
JF  - International Journal of Economics, Finance and Management Sciences
JO  - International Journal of Economics, Finance and Management Sciences
SP  - 192
EP  - 199
PB  - Science Publishing Group
SN  - 2326-9561
UR  - https://doi.org/10.11648/j.ijefm.20180604.17
AB  - 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.
VL  - 6
IS  - 4
ER  -

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