随机利率下的联合保险

Joint-life insurance under random rates of interest

为了简化计算,传统的精算理论均采用固定利率来计算保费.但利率具有随机性,由利率随机性产生的风险对保险公司来说相当大.为此以一对夫妻作为被保险人,研究连生寿险的双随机模型.模型包括夫妻终身寿险以及夫妻养老金等.考虑到保费的实际投资情况以及突发事件对利率的影响,对随机利率采用反射Brownian运动和Poisson过程联合建模,给出了纯保费精算现值的计算公式,并在死亡均匀分布的条件下,得到纯保费精算现值的简洁计算公式.计算实例证明利用该公式进行保费计算可得到理想结果.

To simplify the calculation, traditional actuarial theories usually use fixed interest rate to calculate premium. But in practice, interest rate is stochastic, and the risk resulting from interest rate fluctuation is important to the insurance company. Taking a couple as the insurants, the dual stochastic model of joint-life insurance was researched. The model contains the couple＇s whole life insurance and annuities. Considering the influence of the actual investment of premiums and the outburst cases on interest rate, the random interest rate is decided by both reflected Brownian motion and Poisson process, then the formulas of the actuarial present value of net premium are obtained. Finally, the concise formulas are given on the condition that the death happens uniformly in every policy year. The calculation results show that the formulas are practicable.