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In modern life insurance, Markov processes in continuous time on a finite orat least countable state space have been over the years an important tool forthe modelling of the states of an insured. Motivated by applications indisability insurance, we propose in this paper a model for insurance statesbased on Markov jump processes with more general state spaces. We use thismodel to derive a new type of Thiele's differential equation which e.g. allowsfor a consistent calculation of reserves in disability insurance based ontwo-parameter continuous time rehabilitation rates.

Thiele's Differential Equation Based on Markov Jump Processes with Non-countable State Space