Inference for continuous time multi-state models presents considerable computational difficulties when the process is only observed at discrete time points with no additional information about the state transitions. In fact, for general multi-state Markov model, the evaluation of the likelihood function is possible only via intensive numerical approximations.
The pricing of a Critical Illness insurance requires specific and detailed insur- ance data on healthy and ill lives. However, where the Critical Illness insurance market is small or national commercial insurance data needed for premium esti- mates is unavailable, national health statistics can be a viable starting point for insurance ratemaking purposes, even if such statistics cover the general popu- lation, are aggregate and are reported at irregular intervals.
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