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The multivariate mixed negative binomial regression model with an application to insurance a posteriori ratemaking

INSURANCE MATHEMATICS & ECONOMICS 2021年第PartB期101卷 602-625页

作者： Tzougas, George di Cerchiara, Alice Pignatelli Heriot Watt Univ Dept Actuarial Math & Stat Edinburgh Midlothian Scotland London Sch Econ & Polit Sci Dept Stat London England

This paper is concerned with introducing a family of multivariate mixed negative binomial regression models in the context of a posteriori ratemaking. The multivariate mixed negative binomial regression model can be considered as a candidate model for capturing overdispersion and positive dependencies in multi-dimensional claim count data settings, which all recent studies suggest are the norm when the ratemaking consists of pricing different types of claim counts arising from the same policy. For expository purposes, we consider the bivariate negative binomial-Gamma and negative binomial-Inverse Gaussian regression models. An Expectation-Maximization type algorithm is developed for maximum likelihood estimation of the parameters of the models for which the definition of a joint probability mass function in closed form is not feasible when the marginal means are modelled in terms of covariates. In order to illustrate the versatility of the proposed estimation procedure a numerical illustration is performed on motor insurance data on the number of claims from third party liability bodily injury and property damage. Finally, the a posteriori, or Bonus-Malus, premium rates resulting from the bivariate negative binomial-Gamma and negative binomial-Inverse Gaussian regression model are compared to those determined by the bivariate negative binomial and Poisson-Inverse Gaussian regression models. (C) 2021 Elsevier B.V. All rights reserved.

关键词： multivariate mixed negative binomial regression model EM algorithm A posteriori ratemaking Nonlife insurance Bodily injury and property damage MTPL claim counts

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