中文摘要：

在存在异常值的情况下,非寿险公司应用传统案均赔款法估计准备金常出现估计精度不高的问题。在分析传统案均赔款法中进展因子和结案率估计方法的缺陷之后,引入数学规划法对估计方法进行改进,建立进展因子和结案率的二次规划和目标规划模型,并引入权重因子弱化异常数据对进展因子和结案率估计结果的影响,运用一组流量三角形数据进行实证分析,结果表明：数学规划法可以有效估计进展因子和结案率,弱化异常数据对准备金估计结果的影响。

英文摘要：

In the presence of outlying values, the traditional payments per claim method of es- timating reserving in non-life insurance companies lack accuracy. First, the drawbacks of traditional payments per claim method in progress factors and settlement rate are analyzed briefly.Then introduced mathematical programming into the estimation method, and quadratic programming and objective programming are established to estimate progress factors and settle- ment rate.Meanwhile ,weight is proposed to abate the influence of the outlying values in the esti- mate of the progress factors and settlement rate, and using a set of run off triangle data to provid- ed.The results has shown that the mathematical programming method can effectively estimate progress factor and settlement rate, weakening the influence of outlying values on the estimation of reserves.