Joint modelling of the total amount and the number of claims by conditionals
In the risk theory context, let us consider the classical collective model. The aim of this paper is to obtain a flexible bivariate joint distribution for modelling the couple (S,N), where N is a count variable and S=X1+...+XN is the total claim amount. A generalization of the classical hierarchical model, where now we assume that the conditional distributions of SN and NS belong to some prescribed parametric families, is presented. A basic theorem of compatibility in conditional distributions of the type S given N and N given S is stated. Using a known theorem for exponential families and results from functional equations new models are obtained. We describe in detail the extension of two classical collective models, which now we call Poisson-Gamma and the Poisson-Binomial conditionals models. Other conditionals models are proposed, including the Poisson-Lognormal conditionals distribution, the Geometric-Gamma conditionals model and a model with inverse Gaussian conditionals. Further developments of collective risk modelling are given.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Dionne, G. & Vanasse, C., 1988.
"A Generalization Of Automobile Insurance Rating Models: The Negative Binomial Distribution With A Regression Component,"
Cahiers de recherche
8833, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Dionne, G. & Vanasse, C., 1988. "A Generalization of Automobile Insurance Rating Models: the Negative Binomial Distribution with a Regression Component," Cahiers de recherche 8833, Universite de Montreal, Departement de sciences economiques.
- Spanos,Aris, 1999. "Probability Theory and Statistical Inference," Cambridge Books, Cambridge University Press, number 9780521424080, September.
- José Sarabia & Enrique Castillo & Marta Pascual & María Sarabia, 2007. "Bivariate income distributions with lognormal conditionals," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(3), pages 371-383, December.
- Renshaw, Arthur E., 1994. "Modelling the Claims Process in the Presence of Covariates," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 24(02), pages 265-285, November.
- Pinquet, Jean, 1997. "Allowance for Cost of Claims in Bonus-Malus Systems," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 27(01), pages 33-57, May.
- Smyth, Gordon K. & Jørgensen, Bent, 2002. "Fitting Tweedie's Compound Poisson Model to Insurance Claims Data: Dispersion Modelling," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 32(01), pages 143-157, May.
- Panjer, Harry H. & Willmot, Gordon E., 1981. "Finite Sum Evaluation of the Negative Binomial-Exponential Model," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 12(02), pages 133-137, December.
- J. Pinquet & M. Guillén & C. Bolancé, 2000. "Long-range contagion in automobile insurance data : estimation and implications for experience rating," THEMA Working Papers 2000-43, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
- Frees, Edward W. & Wang, Ping, 2006. "Copula credibility for aggregate loss models," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 360-373, April.
- Katrien Antonio & Jan Beirlant, 2008. "Issues in Claims Reserving and Credibility: A Semiparametric Approach With Mixed Models," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(3), pages 643-676.
- Sarabia, José María & Gómez-Déniz, Emilio & Vázquez-Polo, Francisco J., 2004. "On the Use of Conditional Specification Models in Claim Count Distributions: an Application to Bonus-Malus Systems," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 34(01), pages 85-98, May.
- José María Sarabia & Enrique Castillo & Emilio Gómez-Déniz & Francisco J. Vázquez-Polo, 2005. "A Class of Conjugate Priors for Log-Normal Claims Based on Conditional Specification," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(3), pages 479-495. Full references (including those not matched with items on IDEAS)