一个随机利率下的夫妻综合保险模型

Aggregate life insurance model for couples under random interest rates

针对随机利率下的联合寿险精算问题,建立了一个包括夫妻终身增额寿险,延期支付夫妻增额养老金和储蓄还本部分等综合的联合保险精算模型.考虑到承保人对保费收入的实际投资状况,将利率的连续扩散部分采用了反射布朗运动建模.并在考虑到突发事件会对利率产生的影响,将利率的离散跳跃部分运用了泊松过程建模.给出了均衡净保费的一般表达式和在假设死亡均匀分布条件下均衡纯保费的简洁计算公式.并且通过数值例子说明了模型的正确性与有效性.由于采用半连续式寿险模型计算均衡纯保费,更加符合保险实务的要求,具有较强的实用性与可操作性,有更为广泛的使用范围.

For the combined life insurance issue under stochastic interest rate ,this paper establishes an aggregate life insurance model ,which includes increasing insurance for couple’s life ,increasing pension for couple of deferred payment and repaid principal parts etc .With the influence of the actual investment of premiums ,continuous diffusion section of the random interest rate is decided by reflec‐ted Brow nian motion .Considering the influence of the outburst cases on interest rate ,discrete jump‐ing section of the interest rate is decided by Poisson process .It obtains the formulas of annual level premium ,and the concise expressions of the formula are given in the case that death happens uni‐formly in every policy year .Finally ,the accuracy and validity of the model are verified by numerical examples .The semi‐continuous life insurance model has a wide application and is more suitable to the requirement of insurance practice .