Models for income protection insurance incorporating cause of sickness
Ling, Sing Yee
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The Continuous Mortality Investigation (CMI) of the Institute of Actuaries and the Faculty of Actuaries in the UK established, in CMI Report 12 (1991), a multiple state model consisting of three states (Healthy, Sick and Dead) for the analysis of Income Protection Insurance (IPI) data. The transition intensities between states, estimated using a set of homogeneous male IPI data from 1975-78, are also presented in this re- port. Based on these estimated transition intensities, premium and reserve in respect of IPI business can be calculated. By using this model, in which there is only one Sick state to represent all causes of sickness, a whole portfolio of claims, regardless of their cause of sickness, will be subject to the same termination assumption. With cause of sickness as an important source of heterogeneity among IPI claimants, Cordeiro (1998, 2002) further developed this model so that it can be used to analyse IPI data by cause of sickness and obtained approximations to the cause-specific transition in- tensities defined in this new model. The main application of obtaining cause-specific termination assumptions is in the area of reserving more reliably for a portfolio of claims consisting of different causes of sickness. In this thesis, we present methods and results for the estimation of the recovery and mortality intensities from sick by cause of sickness using IPI data provided by the CMI. There are 70 possible causes of sickness. The recovery intensity model for each cause of sickness assumes a multiplicative structure and is estimated in a structured manner with the use of the Cox model (Cox, 1972) and generalised linear models (GLM). The mortality intensity from sick is modelled using an additive relative survival model in which the excess mortality as a result of being sick is measured relative to the mortality intensity for a standard population. Finally, two applications of the recovery and mortality intensities from sick by cause of sickness are presented.