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2009 | nr 6 | 221--235
Tytuł artykułu

Modelling Insurane Claim Dependencies Using Copulas : an Empirical Investigation

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper focuses on the dependence and, specifically, in what ways, using copula functions, we can include information regarding dependence structure in estimating the distribution of aggregate loss ratio, and how this information influences capital requirements for aggregate underwriting risk of several classes of non-life insurance. The subsequent sections contain basic information concerning copula function, the theorem used for estimating upper and lower bounds for the distribution of the sum of random variables with partial knowledge about dependence structure and the results of empirical research. This research identifies the amount of capital required for aggregate underwriting of risk for two classes of insurance depending on the assumed dependence structure between the loss ratios for those classes. (fragment of text)
Rocznik
Numer
Strony
221--235
Opis fizyczny
Twórcy
  • Cracow University of Economics, Poland
Bibliografia
  • Cossette, H., Denuit, M. and Marceau, E. (2002) "Distributional Bounds for Functions of Dependent Risks". Schweizerische Aktuarvereinigung. Mitteilungen 1.
  • Denuit, M., Genest, С. and Marceau, E. (1999) "Stochastic Bounds on Sums of Dependent Risks. Insurance: Mathematics & Economics 25.
  • Denuit, M. and Scaillet, O. (2004) "Nonparametric Tests for Positive Quadrant Dependence". Journal of Financial Econometrics 2(3).
  • Denuit, M. et al. (2005) Actuarial Theory for Dependent Risks. Measures, Orders and Models. John Wiley & Sons, Ltd.
  • Dhaene, J. et al. (2000) "Comonotonicity and Maximal Stop-loss Premiums". Aktuarvereinigung 2.
  • Dhaene, J. et al. (2002a) "The Concept of Comonotonicity in Actuarial Science and Finance: Theory". Insurance: Mathematics & Economics 31(1).
  • Dhaene, J. et al. (2002b) "The Concept of Comonotonicity in Actuarial Science and Finance: Applications". Insurance: Mathematics & Economics 31(2).
  • Embrechts, P., Höing, A. and Juri, A. (2003) "Using Copulae to Bound the Value-at-risk for Functions of Dependent Risks". Finance and Stochastics 7.
  • Esary, J. D., Proschan, F. and Walkup, D. W. (1967) "Association of Random Variables, with Applications". Annals of Mathematical Statistics 38(5).
  • Financial Conditions and Financial Stability in the European Insurance and Occupational Pension Fund Sector, 2005-2006. Committee of European Insurance and Occupational Pensions Supervisors (CEIOPS). http://vvwvv.ceiops.eu (30 September 2008).
  • Financial Conditions and Financial Stability in the European Insurance and Occupational Pension Fund Sector, 2006-2007, Committee of European Insurance and Occupational Pensions Supervisors (CEIOPS). http://www.ceiops.eu (30 September 2008).
  • Genest, С. and Rivest, L. P. (1993) "Statistical Inference Procedures for Bivariate Archimedean Copulas". Journal of the American Statistical Association 88.
  • Janic-Wróblewska, A., Kallenberg, W. C. M. and Ledwina, T. (2004) "Detecting Positive Quadrant Dependence and Positive Function Dependence". Insurance: Mathematics & Economics 34).
  • Joe, H. (1997) Multivariate Models and Dependence Concepts. Chapman-Hall.
  • Lehmann, E. L. (1966) "Some Concepts of Dependence". Annals of Mathematical Statistics 37(5).
  • Nelsen, R. B. (1999) An Introduction to Copulas. New York: Springer-Verlag.
  • Scaillet, O. (2005) "A Kolmogorov-Smirnov Type Test for Positive Quadrant Dependence. FAME - International Center for Financial Asset Management and Engineering, Research Paper nr 128.
  • Schmeidler, D. (1986) "Integral Representation without Additivity". Proceedings of the American Mathematical Society 97.
  • Shaked, M. (1977) "A Family of Concepts of Dependence for Bivariate Distribution". Journal of the American Statistical Association 72.
  • Sklar, A. (1959) "Fonctions de répartition à n dimensions et leurs marges". Publications de l'Institut de Statistique de l'Université de Paris 8.
  • Williamson, R. and Downs, T. (1990) "Probabilistic Arithmetic. I. Numerical Methods for Calculating Convolutions and Dependency Bounds". International Journal of Approximate Reasoning 4.
  • Yaari, M. E. (1987) "The Dual Theory of Choice under Risk". Econometrica 55.
  • Yanagimoto, T. (1972) "Families of Positively Dependent Random Variables". Annals of the Institute of Statistical Mathematics 24.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000166794213

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