最大熵方法下的纯稳健信度估计

The Pure Robust Credibility Estimation under the Maximum Entropy Method

最大熵方法(MEM)已被广泛运用到保险精算领域,并取得了一定成就,然而,将稳健信度估计与MEM结合起来的相关研究还没有出现,正是致力于这方面的研究,即最大熵方法下的纯稳健信度估计.众所周知,以往的信度公式都要对索赔随机变量X做出一定假设,从而得到信度公式的确切表达形式.对随机变量X没有做出任何假设,也同样得出了信度保费的确切的线性表达形式和两个重要推论.

The maximum entropy method（MEM） has been widely applied to the insurance field and achieved certain a- chievements. However, the research which combines robust credibility estimation and MEM has not appeared until now. This article is dedicated to do some research in this area, namely the pure robust credibility estimation under the maximum entropy method. As we all know, the former credibility formula has to make some assumptions about random variable X to obtain the exact expression of the credibility formula. In this paper, we deduce the exact linear expression for credibility premium and two corollaries on the condition that we make no assumption about X.