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

Published online by Cambridge University Press:  10 May 2011

S. Y. Ling ,
H. R. Waters  and
A. D. Wilkie
H. R. Waters
Affiliation:
Department of Actuarial Mathematics and Statistics, and the Maxwell Institute for the Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, U.K. :, Email: H.R.Waters@hw.ac.uk
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Abstract

In this paper we present methods and results for the estimation and modelling of the recovery intensity for Income Protection (IP) insurance claims, allowing for different causes of claim. We use UK data supplied by the Continuous Mortality Investigation relating to claims paid in the years 1975 to 2002, inclusive. Each claim is classified by one of 70 possible causes according to ICD8.

We group causes where appropriate, and then use the Cox model and generalised linear models to model the recovery intensity.

In two subsequent papers we complete our modelling of IP claim termination rates by discussing the modelling of the mortality of IP claimants.

There are two main reasons why it is useful to incorporate cause of sickness in the modelling of IP claim terminations:

(i) The cause of sickness will be known to the insurer for a claim in the course of payment. A reserve can be set more accurately for such a claim if a model of the termination rates appropriate for this cause is available.

(ii) Different causes of claim will become more or less significant over time. For example, tuberculosis may have been an important cause of sickness in the past, but is likely to be far less significant now; the swine flu pandemic starting in 2009 is likely to have a significant effect on observed aggregate claim termination rates, skewing them towards higher rates at shorter durations. Information about trends in morbidity, together with a model of termination rates by cause of claim, allows future aggregate claim termination rates to be predicted more accurately, reserves to be set at more appropriate levels and policies to be priced more accurately.

One of the covariates included in our models for recovery intensities is Calendar Year. Aggregate recovery intensities have been decreasing over the period considered, 1975 to 2002, and this is generally reflected in the models for recovery intensities by cause of sickness. However, when these intensities are projected for years beyond 2002, the results are not always plausible.

Keywords

Income Protection InsuranceRecoveriesCause of ClaimProportional HazardsCox ModelGeneralised Linear Models
Type
Papers
Information
Annals of Actuarial Science , Volume 4 , Issue 2 , September 2009 , pp. 199 - 239
Copyright
Copyright © Institute and Faculty of Actuaries 2009

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