A Bayesian Approach to Modeling Multivariate Multilevel Insurance Claims in the Presence of Unsettled Claims

Abstract

A Bayesian model for individual insurance claims is proposed which accounts for the multivariate multilevel features of the claims, including multiple claimants for the same event, each of whom may receive benefits under different coverages. A Bayesian approach makes it possible to account for missing values in the covariates and partial information contained in open files, thereby avoiding sampling bias induced when unsettled claims are ignored. For a given claim, the combination of coverages under which payments are made is modeled as a type with multinomial regression. The presence of legal and expert fees follows a logistic regression given the type. The non-zero claim amounts are then modeled with log skewed normal regressions linked by a Student t copula. The Bayesian framework yields a predictive distribution for the amounts paid, including parameter risk and process risk, while handling missing covariates and open files. The approach is illustrated with Accident Benefits car insurance claims from a Canadian company.