The Actuarial Model Under Random Interest

Construct an aggregate model of life insurance with stochastic interest aiming at both the randomness of interest in practice and the importance of stochastic interest in life insurance. The introductions of stochastic interest in the model lessen risk of insurance company. The insurance company can also acquire various insurance products with insurance interest by different combinations of parameters. Establish an optimization model based on aggregate model of life with stochastic interest.On the basis of general insurance risk model, models and results with constant interest are cited. Stochastic interest is considered; and continuous time model and discrete time model with stochastic interest are got; And the probability of ruin is calculated. The distribution of supreme surplus before ruin and the joint distribution of surplus before and at ruin and supreme surplus before ruin, the time that the surplus process reaches a given level x for the first are obtained. This makes the probability of ruin and these consequences have more.significance in practice and propose an important prewarning index of insurance company. In addition, this paper discusses a special life insurance model with stochastic interest and refers interest force as a Brown process. Life annuity and premium of life insurance theory are researched.