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RATEMAKING OF DEPENDENT RISKS

Published online by Cambridge University Press:  06 July 2017

J. M. Andrade e Silva  and
M. de Lourdes Centeno
J. M. Andrade e Silva
Affiliation:
CEMAPRE, ISEG, Universidade de Lisboa E-mail: joaoas@iseg.ulisboa.pt
M. de Lourdes Centeno*
Affiliation:
CEMAPRE, ISEG, Universidade de Lisboa
*
E-Mail: lcenteno@iseg.ulisboa.pt
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Abstract

We start by describing how, in some cases, we can use variance-related premium principles in ratemaking, when the claim numbers and individual claim amounts are independent. We use quasi-likelihood generalized linear models, under the assumption that the variance function is a power function of the mean of the underlying random variable. We extend this approach to the cases where the claim numbers are correlated. Some alternatives to deal with dependent risks are presented, taking explicitly into account overdispersion. We present regression models covering the bivariate Poisson, the generalized bivariate negative binomial and the bivariate Poisson–Laguerre polynomial, which nest the bivariate negative binomial. We apply these models to a portfolio of the Portuguese insurance company Tranquilidade and compare the results obtained.

Keywords

Ratemakingvariance-related premium principlesgeneralized linear modelsquasi-likelihoodbivariate distributions
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 47 , Issue 3 , September 2017 , pp. 875 - 894
Copyright
Copyright © Astin Bulletin 2017 

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References

Bermudez, L. (2009) A priori ratemaking using bivariate Poisson regression models. Insurance: Mathematics & Economics, 44, 135–141. doi:10.1016/j.insmatheco.2008.11.005 Google Scholar
Brockman, M.J. and Wright, M.A. (1992) Statistical motor rating: Making effective use of your data set. Journal of the Institute of Actuaries, 119 (3), 457–543.CrossRefGoogle Scholar
Centeno, M.L. (2005) Dependent risks and excess of loss reinsurance. Insurance: Mathematics & Economics, 37, 229–238. doi:10.1016/j.insmatheco.2004.12.001 Google Scholar
Cossete, H. and Marceau, E. (2000) The discrete-time risk model with correlated classes of businesses. Insurance: Mathematics & Economics, 26, 133–149.Google Scholar
Denuit, M., Maréchal, X., Pitrebois, S. and Walhin, J.-F. (2006) Actuarial Modelling of Claim Counts: Risk Classification, Credibility and Bonus-Malus Scales. New York: Wiley.Google Scholar
Genest, C. and Neslehova, J. (2007) A primer on copulas for count data. ASTIN Bulletin, 37 (2), 475–515.CrossRefGoogle Scholar
Gurmu, S. and Elder, J. (2000) Generalised bivariate count data regression models. Economics Letters, 68, 31–36.Google Scholar
Gurmu, S. and Elder, J. (2007) A simple bivariate count data regression model. Economics Bulletin, 3, 1–10.Google Scholar
Holgate, P. (1964) Estimation for biavariate Poisson distributions. Biometrika, 51, 241–245.Google Scholar
Johnson, L., Kotz, S. and Balakrishnan, N. (1997) Discrete Multivariate Distributions. London: Wiley.Google Scholar
Karlis, D. and Ntzoufras, I. (2005) Bivariate Poisson and diagonal inflated bivariate Poisson regression models in R. Journal of Statistical Software, 14 (10), 1–36.Google Scholar
Kocherlakota, S. and Kocherlakota, K. (2001) Regression in the bivariate Poisson distribution. Communications in Statistics - Theory and Methods, 30 (5), 815–825.Google Scholar
McCullagh, P. and Nelder, J. (1989) Generalized Linear Models, 2nd ed. New York: Chapman & Hall.Google Scholar
Nelder, J.A. and Wedderburn, R.W. (1972) Generalized linear models. Journal of the Royal Statistical Society, A, 135, 370–384.Google Scholar
Shi, P. and Valdez, E. (2014) Multivariate negative binomial models for insurance claim counts. Insurance: Mathematics and Economics,55, 18–29.Google Scholar
Wang, S. (1998) Aggregation of correlated risk portfolios: Mothels and algorithms. Proceedings of the Casualty Actuarial Society, Vol. LXXXV, pp. 848–939.Google Scholar
Whalin, J.F. (2001) Bivariate ZIP models. Biometrical Journal, 43 (2), 147–160.Google Scholar