The Life Insurance Actuarial Model of Paying m Times Annually with the Stochastic Interest Rate

In order to study how the insurance companies claim premiums with the stochastic interest rate, the interest force accumulation function with Wiener process and Poisson process is proposed in this paper. Based on this model, the life insurance actuarial model of paying premiums several times each year is built. And the expression of single net premium, reserve and future loss variance are given. With the hypothesis of uniformly distributed mortality, the built model is applied to the specific insurance practice. By numerical calculation, the relationships between reserve, future loss variance and the times of paying premiums are analyzed. The case mentioned in the model corresponds with the reality, and this model has theoretical and practical value.