Author: F Adékambi

Abstract: In this paper, we consider the Markovian model for the actuarial modelling of health insurance policies
modified by the inclusion of durational effects (the time elapsed since entering a given state) on the
aggregate payment streams, where the force of interest is a diffusion process. We derive differential
equations for the first moment of the present value of the aggregate amount of benefits. We also give
two examples to illustrate our results.
Keywords: Multi-state life insurance; semi-Markov model; counting process; first conditional moment; partial
differential equations; Markov chain