On the graduations associated with a multiple state model for permanent health insurance

The paper puts forward a comprehensive methodology for graduating the transition intensities in a multiple state model for permanent health insurance applications. The approach is based on generalized linear models (GLM) and utilises the data collected and analysed by the U.K. Continuous Mortality Investigation (CMI) Bureau (under the auspices of the Institute and Faculty of Actuaries) in respect of male standard experience of individual PHI policies for the period 1975–1978. The comprehensive and versatile nature of this approach is shown to be applicable to three sets of transition intensities for which data are available: for sickness recovery (as functions of age at sickness onset, x, and duration of sickness, z), for death as sick (also a bivariate function of x and z) and for sickness inception (a function of x only). The full potential of the GLM methodology means that approximations to normality which would lead to complex, iterative methods of fitting can be avoided and that the presence of duplicate policies can be allowed for. A novel feature of the graduation proposed is the introduction of break-point predictors (similar to splines) into the graduation formula, and the method of location of the number and optimum positions of the underlying break-points (or knots).