The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Estimation of Economic Risk Capital of Insurance Company using the Extreme Value Theory

극단치이론을 이용한 보험사 위험자본의 추정

  • 여성칠 (건국대학교 상경대학 응용통계학과) ;
  • 장동한 (건국대학교 상경대학 국제무역학과) ;
  • 이병모 (동양파이낸셜(주) 업무혁신팀)
  • Published : 2007.07.31
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Abstract

With a series of unexpected huge losses in the financial markets around the world recently, especially in the insurance market with extreme loss cases such as catastrophes, there is an increasing demand for risk management for extreme loss exposures due to high unpredictability of those risks. For extreme risk management, to make a maximum use of the information concerning the tail part of a loss distribution, EVT(Extreme Value Theory) modelling nay be the best to analyze extreme values. The Extreme Value Theory is widely used in practice and, especially in financal markets, EVT modelling is getting popular to analyBe the effects of extreme risks. This study is to review the significance of the Extreme Value Theory in risk management and, focusing on analyzing insurer's risk capital, extreme risk is measured using the real fire loss data and insurer's specific amount of risk capital is figured out to buffer the extreme risk.

전 세계적으로 금융시장에서는 예측할 수 없는 대형 사건들이 지속적으로 일어나고 있으며, 특히 보험시장의 경우에는 대재해성(catastrophe)손실 등을 포함한 극단적 사건에 대한 예측이 날이 갈수록 어려워지고 있는바 극단적 위험관리에 대한 필요성이 증대되고 있다. 극단적 위험관리에 있어 분포의 꼬리영역만을 분리하여 그 정보를 최대로 이용하는 방법이 필요한데, 이러한 문제들을 해결하기 위해 극단치들의 움직임을 모형화 하는 소위 극단치 이론(Extreme Value Theory: EVT)을 이용하는 것이 요구된다. 극단치 이론은 현재 여러 분야에서 활용되고 있는데, 특히 금융시장에서는 극단적 변화가 미치는 영향을 분석하기 위해서 극단치 이론을 이용한 금융위험분석을 실시하고 있다. 본 연구에서는 위험관리에 있어서 극단치 이론의 중요성을 검토하고 보험사의 위험자본에 초점을 맞추어 손실 발생의 극단적 위험을 측정하고 이에 대비한 위험자본의 적정규모를 측정하여 보았다.

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References

  1. Balkema, A. A. and de Haan, L. (1974). Residual life time at great age, The Annals of Probability, 2, 792-804 https://doi.org/10.1214/aop/1176996548
  2. Coles, S. G. (2001). An Introduction to Statistical Modeling of Extreme Values, Springer-Verlag, London
  3. Corradin, S. (2003). Economic risk capital and reinsurance: an extreme value theory's application to fire claims on an insurance company, Astin Bulletin
  4. Embrechts, P., Klupppelberg, C. and Mikosh, T. (1997). Modelling Extremal Events for Insurance and Finance, Springer-Verlag, Berlin
  5. Fisher, R. A. and Tippett, L. H. C. (1928). Limiting forms of the frequency distribution of the largest or smallest member of a sample, Proceedings of the Cambridge Philosophical Society, 24, 180-190
  6. Hill, B. M. (1975). A simple general approach to inference about the tail of a distribution, Annals of Statistics, 3, 1163-1173 https://doi.org/10.1214/aos/1176343247
  7. Hogg, R. V. and Klugman, S. A. (1984). Loss Distributions, Wiley
  8. Hosking, J. R. M. and Wallis, J. R. (1987). Parameter and quantile estimation for the generalized Pareto distribution. Technometrics, 29, 339-349 https://doi.org/10.2307/1269343
  9. Hurlimann, W. (2004). On the economic risk capital of portfolio insurance, International Journal of Mathematics and Mathematical Sciences, 41, 2209-2218
  10. Jenkinson, A. F. (1955). The frequency distribution of the annual maximum (or minimum) values of meteorological events. Quarterly Journal of the Royal Meteorological Society, 81, 158-172 https://doi.org/10.1002/qj.49708134804
  11. McNeil, A. J. (1997). Estimating the Tails of Loss Severity Distribution using Extreme Value Theory, Astin Bulletin, 27, 117-137 https://doi.org/10.2143/AST.27.1.563210
  12. Pickands, J. (1975). Statistical inference using extreme order statistics, Annals of Statistics, 3, 119-131 https://doi.org/10.1214/aos/1176343003
  13. Reiss, R. D. and Thomas, M. (2001). Statistical Analysis of Extreme Values, 2nd ed., Birkhauser Verlag, Basel
  14. von Mises, R. (1936). La distribution de la plus grande de n valeurs. Rev. Math. Union Interbalcanique, 1, 141-160. Reproduced in Selected Papers of Richard von Mises. American Mathematical Society (1964), 2, 271-294
  15. Yeo, S. C. (2006). Performance analysis of VaR and ES based on extreme value theory, The Korean Communications in Statistics, 13, 389-407 https://doi.org/10.5351/CKSS.2006.13.2.389