A Class of Variable Payment Life Insurance Model with the Stochastic Interest Rate

In order to decrease the pricing risk of the insurance companies caused by the variable interest rate, a class of variable payment life insurance model with stochastic interest rate is proposed in this paper. By introducing a n-years variable payment endowment insurance model, a series of traditional actuarial models can be gained by changing parameters. Then, the single net premium and the level net premium are calculated with the interest force accumulated function modelled as a reflected Brownian motion and a reflected Brownian motion combined with Poisson process. Finally, the corresponding expressions of the single net premium and the level net premium with the hypothesis of de Moivre mortality are presented.