寿险定价的线性优化模型

实际的金融市场中存在多种不同期限的利率。在定义最大累积函数的基础上建立了一个称为“收支问题”的线性规划模型，这个模型的最优值刻画了合理安排保费资金的投资期限所能够达到的最大保险支付水平，从而给出了多利率条件下寿险费率的计算依据。使用局部优化方法证明了收支问题最优解的两个性质，这些性质说明在满足保险支出的条件下，保险收入资金应该优先考虑期限较长（即利率较大）的投资。对于典型的寿险产品模型，给出了最优解的结构，针对两个具体实例列出了计算结果。结果表明，在保险费率的计算中，起主要作用的是最大期限的利率，其次是不同利率的一个综合水平。

Linear Optimization Model for Life Insurance Pricing

There are various interest rates of different terms in the actual financial markets. In order to calculate the life insurance rates under the condition of multiple interest rates, a linear programming model which is called "Income-outcome problem(IOP)" was established on the basis of the definition of maximum accumulation function, and its optimal value describes the maximum level of insurance payment that can be achieved through the rational arrangement of investment term of premium funds. Using local optimization method, two properties of the optimal solution of IOP are proved, and these properties show that the premium income fund should gives priority to the investment which has longer term (that is, larger interest rates) on the condition of meeting the insurance expenditures. For some typical life insurance product model, we give the structure of the optimal solution and list the calculated results of premium rate of two specific examples. The results show that the main factor in the calculation of premium rates is the longest term interest rate, followed by an comprehensive level of the different interest rates. The model of this paper also provides the basis for creating generalized theory of interest under the condition of multiple interest rates.