熵与大偏差及保险定价

Entropy,large deviation and insurance pricing

为了更加合理的解决保险定价问题,引入信息论中的熵和概率理论中的大偏差,对一般保费计算方法进行了修正。结果表明:最大熵原理只考虑了具有最大熵的概率分布,而在大偏差框架中,考虑了所有的概率分布,此时的熵描绘了随着实验次数的增加,概率分布的收敛情况;若只知道概率分布的不完全信息,最小化叉熵,得到最小叉熵优化模型,模型的解可调整保费。调整后的保费计算方法既建立在经验概率分布基础上,又不完全依赖经验概率分布,具有更好的实用性。

In order to make insurance pricing more reasonable, the entropy in information theory and the large deviation in probability theory are introduced to adjust the premium principle. The results show that the maximum entropy principle only considers the probability distribution with the maximum entropy. However, all distributions are taken into account in large deviation field. The entropy describes the convergence of probability distribution when the experiment numbers are increased. Under the incomplete information of the probability distribution, the minimum cross-entropy optimization model is obtained. The solution of the model may be used to adjust the premium. The adjusted premium is based on the experiential probability distribution, but incompletely. So, the new premium will be more practical.