A two-component copula with links to insurance

S. Ismail 1 , G. Yu 2 , G. Reinert 1 ,  and T. Maynard 2
  • 1 Department of Statistics, 1 South Parks Road, , Oxford , UK
  • 2 Exposure Management Team, Lloyd’s of London, , London, UK

Abstract

This paper presents a new copula to model dependencies between insurance entities, by considering how insurance entities are affected by both macro and micro factors. The model used to build the copula assumes that the insurance losses of two companies or lines of business are related through a random common loss factor which is then multiplied by an individual random company factor to get the total loss amounts. The new two-component copula is not Archimedean and it extends the toolkit of copulas for the insurance industry.

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  • [1] Arnold, B. C. (2014). Univariate and multivariate Pareto models. J. Stat. Distrib. Appl. 1:11.

  • [2] Ben Ghorbal, N., C. Genest, and J. Nešlehová (2009). On the Ghoudi, Khoudraji, and Rivest test for extreme-value dependence. Canad. J. Statist. 37(4), 534-552.

  • [3] Benjamini, Y. and D. Yekutieli (2001). The control of the false discovery rate in multiple testing under dependency. Ann. Statist. 29(4), 1165-1188.

  • [4] Berg, D. (2009). Copula goodness-of-fit testing: an overview and power comparison. Eur. J. Financ. 15(7-8), 675-701.

  • [5] Cox, C., H. Chu, M. Schneider, and A. Muñoz (2007). Parametric survival analysis and taxonomy of hazard functions for the generalized gamma distribution. Stat. Med. 26(23), 4352-4374.

  • [6] Durante, F. and C. Sempi (2010). Copula theory: An introduction. In P. Jaworski, F. Durante, W. Härdle, and T. Rychlik (Eds.), Copula Theory and Its Applications, pp. 3-31. Springer, Berlin.

  • [7] Durante, F. and C. Sempi (2015). Principles of Copula Theory. CRC press, Boca Raton FL.

  • [8] Embrechts, P., C. Klüppelberg, and T. Mikosch (1997). Modelling Extremal Events. For Insurance and Finance. Springer-Verlag, New York.

  • [9] Embrechts, P., F. Lindskog, and A. McNeil (2003). Modelling dependencewith copulas and applications to riskmanagement. In S.T. Rachev (Ed.), Handbook of Heavy Tailed Distributions in Finance, pp. 329-384. Elsevier Science, Amsterdam.

  • [10] Foss, S., D. Korshunov, and S. Zachary (2011). An Introduction to Heavy-Tailed and Subexponential Distributions. Springer, New York.

  • [11] Glen, A. (2011). On the inverse gamma as a survival distribution. J. Quality Technology 43(2), 158-166.

  • [12] Gudendorf, G. and J. Segers (2010). Extreme-Value copulas. In P. Jaworski, F. Durante, W. Härdle, and T. Rychlik (Eds.), Copula Theory and Its Applications, pp. 127-145. Springer, Heidelberg.

  • [13] Jaworski, P., F. Durante,W. K. Hardle, and T. Rychlik, editors (2010). Copula Theory and Its Applications. Springer, Heidelberg.

  • [14] Nelsen, R. B. (2006). An Introduction to Copulas. Second edition. Springer, New York.

  • [15] Schmidt, T. (2007). Coping with copulas. In J. Rank (Ed.), Copulas - From Theory to Applications in Finance, pp. 3-34. Risk Books, London.

  • [16] Weiß, G. (2014). Identifying mixture copula components using outlier detection methods and goodness-of- t tests. J. Risk 16(4), 61-101.

  • [17] Wile, R. (2012). The 11 most expensive insurance losses in recent history. Business Insider. Available at http://www.businessinsider.com/the-11-most-expensive-insurance-losses-in-recent-history-2012-2.

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Dependence Modeling aims to provide a medium for exchanging results and ideas in the area of multivariate dependence modeling. Topics include Copula methods, environmental sciences, estimation and goodness-of-fit tests, extreme-value theory, limit laws, mass transportations, measures of association, multivariate distributions and tests, quantitative risk management, risk assessment, risk models, risk measures and stochastic orders and time series.

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