A time‐continuous markov chain interest model with applications to insurance

Abstract

Abstract The force of interest is modelled by a homogeneous time‐continuous Markov chain with finite state space. Ordinary differential equations are obtained for expected values of various functionals of this process, in particular for moments of present values of payment streams that may be deterministic or, possibly, also stochastic and driven by a time‐continuous Markov chain. The homogeneity of the interest process gives rise to explicit formulae for expected values of some stationary functionals, e.g. moments of a perpetuity. Applications are made to some standard forms of insurance.