Modelling the Claim Duration of Income Protection Insurance Policyholders using Parametric Mixture Models

Abstract

ABSTRACT

This paper considers the modelling of claim durations for existing claimants under income protection insurance policies. A claim is considered to be terminated when the claimant returns to work. Data used in the analysis were provided by the Life and Risk Committee of the Institute of Actuaries of Australia. Initial analysis of the data suggests the presence of a long-run probability, of the order of 7%, that a claimant will never return to work. This phenomenon suggests the use of mixed parametric regression models as a description of claim duration which include the prediction of a long-run probability of not returning to work. A series of such parametric mixture models was investigated, and it was found that the generalised F mixture distribution provided a good fit to the data and also highlighted the impact of a number of statistically significant predictors of claim duration.