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Multivariate Extreme Value Theory And Its Usefulness In Understanding Risk

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  • Debbie Dupuis
  • Bruce Jones

Abstract

This paper gathers recent results in the analysis of multivariate extreme values and illustrates their actuarial application. We review basic and essential background on univariate extreme value theory and stochastic dependence and then provide an introduction to multivariate extreme value theory. We present important concepts for the analysis of multivariate extreme values and collect research results in this area. We draw particular attention to issues related to extremal dependence and show the importance of model selection when fitting an upper tail copula to observed joint exceedances. These ideas are illustrated on four data sets: loss amount and allocated loss adjustment expense under insurance company indemnity claims, lifetimes of pairs of joint and lastsurvivor annuitants, hurricane losses in two states, and returns on two stocks. In each case the extremal dependence structure has an important financial impact.

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  • Debbie Dupuis & Bruce Jones, 2006. "Multivariate Extreme Value Theory And Its Usefulness In Understanding Risk," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(4), pages 1-27.
    • Handle: RePEc:taf:uaajxx:v:10:y:2006:i:4:p:1-27
    DOI: 10.1080/10920277.2006.10597411
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    Citations

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    Cited by:

    1. Zhengjun Zhang, 2009. "On approximating max-stable processes and constructing extremal copula functions," Statistical Inference for Stochastic Processes, Springer, vol. 12(1), pages 89-114, February.
    2. Queensley C Chukwudum, 2018. "Extreme Value Theory and Copulas: Reinsurance in the Presence of Dependent Risks," Working Papers hal-01855971, HAL.
    3. Kellner, Ralf & Gatzert, Nadine, 2013. "Estimating the basis risk of index-linked hedging strategies using multivariate extreme value theory," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4353-4367.
    4. Carlin C. F. Chu & Simon S. W. Li, 2024. "A multiobjective optimization approach for threshold determination in extreme value analysis for financial time series," Computational Management Science, Springer, vol. 21(1), pages 1-14, June.
    5. Xiaohu Li & Jintang Wu & Jinsen Zhuang, 2015. "Asymptotic Multivariate Finite-time Ruin Probability with Statistically Dependent Heavy-tailed Claims," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 463-477, June.
    6. Li, Deyuan & Peng, Liang, 2009. "Goodness-of-fit test for tail copulas modeled by elliptical copulas," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1097-1104, April.
    7. Eling, Martin, 2012. "Fitting insurance claims to skewed distributions: Are the skew-normal and skew-student good models?," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 239-248.
    8. Dutfoy Anne & Parey Sylvie & Roche Nicolas, 2014. "Multivariate Extreme Value Theory - A Tutorial with Applications to Hydrology and Meteorology," Dependence Modeling, De Gruyter, vol. 2(1), pages 1-19, June.

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