Estimation of the Upper Tail Dependence Coefficient for Insurance Loss Data Using an Empirical Copula-Based Approach
Considerable focus in the world of insurance risk quantification is placed on modeling loss values from lines of business (LOBs) that possess upper tail dependence. Copulas such as the Joe, Gumbel and Student-t copula may be used for this purpose. The copula structure imparts a desired level of tail dependence on the joint distribution of claims from the different LOBs. Alternatively, practitioners may possess historical or simulated data that already exhibit upper tail dependence, through the impact of catastrophe events such as hurricanes or earthquakes. In these circumstances, it is not desirable to induce additional upper tail dependence when modeling the joint distribution of the loss values from the individual LOBs. Instead, it is of interest to accurately assess the degree of tail dependence already present in the data. The empirical copula and its associated upper tail dependence coefficient are presented in this paper as robust, efficient means of achieving this goal.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1336362Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4446
 T. Schmidt, "Coping with copulas,” in Copulas: From Theory to Application in Finance 1st ed. J. Rank, Ed. London: Risk Books, 2006.
 S. D. Bolboacă and L. J ӓntschi, "Pearson versus Spearman, Kendal’s Tau Correlation Analysis on the Structure Activity Relationships of Biologic Active Compounds,” Leonardo Journal of Sciences, no. 9, pp. 179-200, July-December 2006.
 S. Lee, "Formula from Hell,” Forbes, May 2009.
 S. Demarta and A. McNeil, "The t Copula and Related Copulas,” International Statistical Review, vol. 73, no. 1, pp. 111-129, April 2005.
 G. G. Venter, "Tails of Copulas,” Proceedings of Casualty Actuarial Society vol. 89, no. 171, pp.68-113, Mar. 2002.
 R. A. Shaw, A. D. Smith, and G. S. Spivak, "Measurement and modelling of dependencies in economic capital. A discussion paper,” The Institute and Faculty of Actuaries Sessional Meeting, paper 10,pp. 54-71, May 2010.
 P. Embrechts, F. Lindskog, and A. McNeil, "Modelling Dependence with Copulas and Applications to Risk Management,” in Handbook of Heavy Tail Distributions in Finance: Handbooks in Finance. Revised ed. vol. 1, S. T. Rachev, Ed. Amsterdam: North-Holland/Elsevier, 2003, pp. 329-384.
 A. Sklar, "Fonctions de répartition à n dimensions et leurs marges", Publ. Inst. Statist. Univ. Paris, vol.8, pp. 229–231, 1959.
 G. Frahm, M. Junker, and R. Schmidt, "Estimating the tail-dependence coefficient: Properties and pitfalls,” Insurance: Mathematics and Economics, vol. 37, no. 1, pp. 80-100, 2005.
 M. Fischer and I. Klein, "Some results on weak and strong tail dependence coefficients for means of copulas, Discussion paper,” Friedrich-Alexander-University Erlangen-Nuremburg, Chair of Statistics and Economics, No. 78, 2007.
 P. J. Sweeting and F. Fotiou, "Calculating and communicating tail association and the risk of extreme loss. A discussion paper,” The Institute and Faculty of Actuaries Sessional Research Discussion Paper, pp.3-20, Sept. 2011.
 R Core Team. "R: A language and environment for statistical computing”. R Foundation for Statistical Computing, Vienna, Austria, 2012.
 T. Hayfield and J. S. Racine, "Nonparametric econometrics: the np package”, Journal of Statistical Softwarevol. 27, no.5., 2008.