The multivariate mixed Negative Binomial regression model with an application to insurance a posteriori ratemaking

George Tzougas and Alice Pignatelli di Cerchiara

Insurance: Mathematics and Economics, 2021, vol. 101, issue PB, 602-625

Abstract: 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.

Keywords: Multivariate mixed Negative Binomial regression model; EM algorithm; A posteriori ratemaking; Nonlife insurance; Bodily injury and property damage MTPL claim counts (search for similar items in EconPapers)
JEL-codes: C13 C63 G22 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:101:y:2021:i:pb:p:602-625

DOI: 10.1016/j.insmatheco.2021.10.001

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