Hierarchical generalized linear models, correlation and a posteriori ratemaking
Physica A: Statistical Mechanics and its Applications（2023）
Abstract
Insurance pricing is the premium set by the insurance companies. Hierarchical generalized linear models (HGLM) particularly those dealing with count data and their application to insurance pricing are investigated. In the context of car insurance a posteriori ratemaking, the Poisson-gamma HGLM and the negative binomial-beta HGLM are compared. It is shown that contrary to the HGLM Poisson-gamma, the negative binomial-beta HGLM fits the correlation between successive claim numbers of a given insured, which generates a significant difference of the resulting a posteriori premiums. Simulations and an application based on a real portfolio of car insurance are carried out to support the theoretical results.
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Key words
A posteriori ratemaking,Count data,Computational statistics,Mixture of Poisson distribution,Mixture of binomial negative distribution,Hierarchical generalized linear model
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