Application Of Linear Optimization To Life Actuarial Science

There are various interest rates in the actual financial markets. Under the assumption that term structure of interest rates at different times has the same form, we first discuss its properties and make some reasonable assumptions. On this basis, a linear programming model is established. Its optimal solution describes the maximum level of insurance payment that can be achieved through the rational arrangement of investment term of premium funds under a fixed term structure of interest rate, and gives the calculation basis of life insurance rate under the condition of multiple interest rates. According to the properties of the term structure of interest rate, we simplify the linear programming model and give some properties of the optimal solution. These properties show that the term structure of investment of premium income fund corresponding to the optimal solution always 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 describe the basic structure of the optimal solution, give the binary search method to calculate the premium rate and list the calculated results for two specific examples. The results show that the main factor in the calculation of premium rates is the longest term interest rate, followed by a comprehensive level between different interest rates, which is related to the insurance payments.