This paper surveys some statistical models of survival data. A basic model of a random lifetime is defined, and censoring is introduced. Methods based on observations of small segments of lifetimes are compared. Markov and semi-Markov (multiple state) models are recommended as well-understood and flexible models well suited to actuarial data. A Poisson model is discussed as an approximation to a two state model, while traditional Binomial-type models are shown to be more restricted and less tractable than multiple state models.

Counting processes and their compensators are introduced at a heuristic level. The martingale property of stochastic integrals with respect to a compensated counting process leads to moment estimates and asymptotic normal distributions for statistics arising in multiple state, non-parametric and semi-parametric models. The place of survival models in actuarial education is discussed.

Cordeiro (2002a) has presented a multiple state model for Income Protection (formerly known as Permanent Health Insurance) which enables us to analyse claims by cause of disability. In that paper average claim durations conditioned on recovery have been calculated.

Since, when an Income Protection claim is reported, the insurance company never knows whether it will end in recovery, in death or in expiry, to analyse only average claim durations conditioned on recovery could be misleading, specially for the people responsible for the claims control process.

The main purpose of this paper is to calculate average claim durations conditioned on death and average claim durations not conditioned on any particular mode of claim termination. We calculate these claim durations for different deferred periods, causes of disability and ages at the beginning of sickness and we analyse the results obtained.

The main objective of this paper is to measure the process error for a portfolio of independent disability insurance policies in a multiple state modelling context. We consider the calculation of premiums for a portfolio of income protection insurance policies in a stochastic environment represented both by random transitions in the underlying multiple state model and random external economic factors in the form of stochastic investment returns and inflation. We also investigate the sensitivity of the process error to the level of volatility incorporated in a given model using suitably defined risk measures. We then draw conclusions and identify possible avenues for future research.

The purpose of this paper is to obtain approximations to the transition intensities defined for a multiple state model for Permanent Health Insurance (PHI) which enables us to analyse PHI claims by cause of disability.

The approximations to the transition intensities are obtained using a set of PHI data classified by 18 sickness categories and the graduations of the transition intensities defined for a simpler model proposed in Continuous Mortality Investigation Reports, 12 (1991).

In order to derive the approximations to the recovery and mortality of the sick intensities for our model, we carry out tests of hypotheses based on the distributions of average sickness durations. The approximations to the sickness intensities are obtained by estimating a statistical model for the number of claim inceptions, which can be formulated as a generalized linear model.

The paper considers a number of methods of estimating the work time lost due to sickness, unemployment and stoppages. The most satisfactory approach suggested is based on a multiple state working life table. Numerical examples of the measurement of work time lost are provided for particular application to the actuarial assessment of damages (arising out of personal injury or fatal accident). Other applications, including the pricing of unemployment insurance, are also discussed.