  We derive a general multiple state model for critical illness insurances. In
contrast to the classical model, we take into account that the probability of
death for a dread disease sufferer may depend on the duration of the disease,
and the payment of benefits associated with a severe disease depends not only
on the diagnosis but also on the disease stage. We apply the introduced model
to the analysis of a critical illness insurance against the risk of lung
cancer. Based on the real data for the Lower Silesian Voivodship in Poland, we
estimate the transition matrix, related to the discrete-time Markov model. The
obtained probabilistic structure of the model can be directly used to cost not
only critical illness insurances and life insurances with accelerated death
benefits option, but also to viatical settlement contracts.
