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Bivariate Mixed Poisson and Normal Generalised Linear Models with Sarmanov Dependence An Application to Model Claim Frequency and Optimal Transformed Average Severity

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The aim of this paper is to introduce dependence between the claim frequency and the average severity of a policyholder or of an insurance portfolio using a bivariate Sarmanov distribution, that allows to join variables of different types and with different distributions, thus being a good candidate for modeling the dependence between the two previously mentioned random variables. To model the claim frequency, a generalized linear model based on a mixed Poisson distribution -like for example, the Negative Binomial (NB), usually works. However, finding a distribution for the claim severity is not that easy. In practice, the Lognormal distribution fits well in many cases. Since the natural logarithm of a Lognormal variable is Normal distributed, this relation is generalised using the Box-Cox transformation to model the average claim severity. Therefore, we propose a bivariate Sarmanov model having as marginals a Negative Binomial and a Normal Generalized Linear Models (GLMs), also depending on the parameters of the Box-Cox transformation. We apply this model to the analysis of the frequency-severity bivariate distribution associated to a pay-as-you-drive motor insurance portfolio with explanatory telematic variables.

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cc-by (c) Alemany Leira, Ramon et al., 2021

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Articles publicats en revistes  (Econometria, Estadística i Economia Aplicada)

# metadata.dc.title[].value
Bivariate Mixed Poisson and Normal Generalised Linear Models with Sarmanov Dependence An Application to Model Claim Frequency and Optimal Transformed Average Severity