Reserves in the multi-state health insurance model with stochastic interest of diffusion type

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