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

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.

Modelling Income Protection Claim Termination Rates by Cause of Sickness I: Recoveries

“…However, this power comes at a price ö the basic assumption, that the effect of each covariate is multiplicative, is very strong. It is interesting to note that in relation to the modelling of claim termination rates for Australian IP data, Pitt (2007) reported that there were clear violations of the assumption of proportional hazards for some of the key rating factors. However, Pitt did not allow for the possibility of duration-varying effects, i.e.…”

Regression Quantile Analysis of Claim Termination Rates for Income Protection Insurance

“…In order to make the interpretation of results simpler, we restrict ourselves in this paper to the consideration of the effect of age, occupation class (C or D vs A or B). (See Pitt (2006a) for a description of occupation classes) and deferred period (greater than or equal to 28 days or less than 28 days).…”

“…A censored regression quantile model was fitted using the entire dataset of claim durations described in Pitt (2006a). The R (2005) command used to fit the model is:…”

“…A model considered in Pitt (2006a) which is often used in survival analysis is the Cox regression model, (Cox, 1972). This model estimates the impact of rating factors such as age and occupation class on the dependent variable, claim duration, by considering the impact of these rating factors collectively across all quantiles of the claim duration distribution.…”

“…In the context of disability income insurance claim termination rates, Pitt (2006a) gives an illustration of how various insured characteristics impact claim termination rates differently at different quantiles of the distribution of claim duration. In that paper, the use of mixture models showed that the smoker status, which had not been included in previous Australian industry tables for claim termination, has a statistically significant impact on the probability that an IP insurance claim will continue indefinitely and that the claimant will never return to work.…”