A Heavy-Tailed and Overdispersed Collective Risk Model

Insurance data can be asymmetric with heavy tails, causing inadequate adjustments of the usually applied models. To deal this issue, a hierarchical model for collective risk tails claims distributions that also takes into account overdispersion number is proposed. In particular, distribution logarithm aggregate value assumed to follow Student t distribution. Additionally, incorporate possible overdispersion, modeled as having negative binomial Bayesian decision theory invoked calculate fair premium based on modified absolute deviation utility. An application health insurance set presented together some diagnostic measures identify excess variability. The variability are analyzed using marginal posterior predictive premiums according competitive Finally, simulation study carried out assess capability and adequacy estimation procedure.