## Project CEMAPRE internal

Title | Application of bivariate discrete distributions to actuarial modelling |

Participants | João Andrade e Silva (Principal Investigator), Maria de Lourdes Centeno |

Summary | In the last two decades, actuaries have used Generalized Linear Models (GLM), see Nelder and Wedderburn (1972) or Denuit et al (2006) to deal with many actuarial problems, like ratemaking or claim reserving. More recently dependence among risks has been one of the most popular subjects [See Denuit et al (2006)]. Dependence modeling has mostly been treated by the use of copulas for continuous data. However in insurance, dependence between risks is often due to the claim numbers. In 2016 we analyzed ratemaking of dependent risks by modelling the number of claims using a bivariate Poisson, a generalized bivariate negative binomial and a bivariate Poisson-Laguerre polynomial distributions. We intend to pursue our approach considering now the same distributions but with zero and diagonal inflated values, phenomena which occur in many lines of insurance business. References: Gurmu, S. and Elder, J. (2000) Generalised bivariate count data regression models. Economics Letters, pp.31-36. Gurmu, S. and Elder, J. (2007) A simple bivariate count data regression models. Economics Bulletin, 3, pp.1-10. Karlis, D. and Ntzoufras, I. (2005) Bivariate Poisson and Diagonal Inflated Bivariate Poisson Regression Models in R, Journal of Statistical Software, 14/10, pp 1-36. Kocherlakota, S. and Kocherlakota, K.(2001) Regression in the bivariate Poisson distribution, Communications in Statistics - Theory and Methods, 30/5, pp 815-825. Nelder, J.A. and Wedderburn, R.W.M. (1972) Generalized Linear Models, Journal of the Royal Statistical Society, Serie A, vol 135,2, pp 370-384. Denuit, M. Marchal, X., Pitrebois, S. and Walhin, J-F. (2006) Actuarial Modelling of Claim Counts: Risk Classification, Credibility and Bonus-Malus Systems, Wiley. |