Total loss estimation using copula-based regression models

Insurance: Mathematics and Economics

Volumn 53, Issue 3, 2013, Pages 829-839

  Krämer, Nicole ^a   Brechmann, Eike C ^a   Silvestrini, Daniel ^a   Czado, Claudia ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Claim size; Dependence modeling; Generalized linear model; Number of claims; Policy loss

Indexed keywords

EID: 84921852352     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.insmatheco.2013.09.003     Document Type: Article

References (29)

1. Aas, K., Czado, C., Frigessi, A., Bakken, H., Pair-copula constructions of multiple dependence. Insurance: Mathematics & Economics 44 (2009), 182–198.
2. Brechmann, E., Schepsmeier, U., Modeling dependence with C- and D-vine copulas: the R-package CDVine. Journal of Statistical Software 52:3 (2013), 1–27.
3. Czado, C., Kastenmeier, R., Brechmann, E., Min, A., A mixed copula model for insurance claims and claim sizes. Scandinavian Actuarial Journal(4), 2012, 278–305.
4. De Jong, P., Modeling dependence between loss triangles using copulas. Technical Report., 2009, Macquarie University.
5. De Leon, A.R., Wu, B., Copula-based regression models for a bivariate mixed discrete and continuous outcome. Statistics in Medicine 30 (2011), 175–185.
6. Frees, E., Valdez, E., Understanding relationships using copulas. North American Actuarial Journal 2 (1998), 1–25.
7. Gschlößl, S., Czado, C., Spatial modelling of claim frequency and claim size in non-life insurance. Scandinavian Actuarial Journal 2007 (2007), 202–225.
8. Haberman, S., Renshaw, A.E., Generalized linear models and actuarial science. The Statistician 45 (1996), 407–436.
9. Hothorn, T., Bretz, F., Westfall, P., Simultaneous inference in general parametric models. Biometrical Journal 50 (2008), 346–363.
10. Joe, H., Multivariate Models and Dependence Concepts. 1997, Chapman & Hall, London.
11. Joe, H., Xu, J., The estimation method of inference functions for margins for multivariate models. Technical Report, Department of Statistics, University of British Colombia 166., 1996.
12. Klugman, S., Parsa, R., Fitting bivariate loss distributions with copulas. Insurance: Mathematics & Economics 24 (1999), 139–148.
13. Krämer, N., Silvestrini, D., 2012. CopulaRegression: bivariate Copula based regression models, version 0.1-3.
14. Lehmann, E., Casella, G., Theory of Point Estimation. second ed., 1998, Springer, New York.
15. Lundberg, F., Approximerad Framställning Afsannollikhetsfunktionen. II. återförsäkring af Kollektivrisker. 1903, Almqvist & Wiksells Boktr., Uppsala.
16. McNeil, A.J., Frey, R., Embrechts, P., Quantitative Risk Management: Concepts Techniques and Tools. 2005, Princeton University Press, Princeton.
17. Nelsen, R.B., An Introduction to Copulas. second ed., 2006, Springer, Berlin.
18. Panagiotelis, A., Czado, C., Joe, H., Pair copula constructions for multivariate discrete data. Journal of the American Statistical Association 107 (2012), 1063–1072.
19. Schepsmeier, U., Stöber, J., Derivatives and Fisher information of bivariate copulas. Statistical Papers, 2013, 10.1007/s00362-013-0498-x.
20. Serfling, R., Approximation Theorems of Mathematical Statistics. 1980, John Wiley & Sons, New York.
21. Sklar, A., Fonction de répartition à n dimensions et leurs marges. Publications de l'Institut de Statistique de l'Université de Paris 8 (1959), 229–231.
22. Song, P., Multivariate dispersion models generated from Gaussian copula. Scandinavian Journal of Statistics 27 (2000), 305–320.
23. Song, P.X.K., Correlated Data Analysis: Modeling, Analytics, and Applications, first ed. Springer Series in Statistics, vol. 365, 2007, Springer, New York.
24. Song, P.K., Fan, Y., Kalbfleisch, J., Maximization by parts in likelihood inference. Journal of the American Statistical Association 100 (2005), 1145–1166.
25. Song, P.X.K., Li, M., Yuan, Y., Joint regression analysis of correlated data using Gaussian copulas. Biometrics 65 (2009), 60–68.
26. Stöber, J., Czado, C., Hong, H.G., Ghosh, P., 2012. Modeling multiple chronic diseases in the elderly: longitudinal patterns identified by copula design for mixed responses. Preprint.
27. Vuong, Q., Ratio tests for model selection and non-nested hypotheses. Econometrica 57 (1989), 307–333.
28. Yee, T.W., The VGAM package for categorical data analysis. Journal of Statistical Software 32 (2010), 1–34.
29. Yee, T.W., Wild, C.J., Vector generalized additive models. Journal of the Royal Statistical Society: Series B 58 (1996), 481–493.