Another Approach to Stochastic Thiele’s Differential Equation in Life Insurance and Applications

The paper provides the local square integrable martingale representation of martingale M（t） = E（V₀|F_t） to the situation where a life insurance policy is modelled as a time-inhomogeous Markov chain with a finite state space under more general assumption than Norberg’s, which is hot similar to Mϕller. As a byproduct, stochastic Thiele’s differential equation is obtained, moreover, a general representation is given for the variance of the losses. At last, the application of stochastic Thiele’s differential equation is illustrated by an example relating to widow’s pension on which the payments depend on reserves.