基于平衡损失函数和最大熵方法的信度估计

Reliability Estimation Based on Balanced Loss Function and Maximum Entropy Method

在保险精算领域,信度理论是一种计算保费的经验模型,根据过去的风险和数据,精算师可利用信度理论计算可行的保费.而事实上,过去几期的保费并不服从某种具体的分布,因此引入最大熵方法,在仅已知部分历史信息的前提下,对保费进行合理推断.此外,考虑到正负误差引起的损失不同,采用了一种非对称损失函数——平衡损失函数.基于该平衡函数,经过最大熵优化,得到了信度保费的估计.最后,通过数值模拟,验证了此方法比经典信度估计更优.

In actuarial field,the reliability theory is an empirical model of calculating premium.According to the past risk and data,actuaries can use the reliability theory to calculate feasible premium.In reality,the premium of the past few periods is not subject to a specific distribution,so we introduce the maximum entropy method,this method can be used to infer the reasonable premium under the premise of only known partial historical information.In addition,considering the difference of loss caused by positive and negative errors,we use an asymmetric loss function-Balance loss function in this paper.Based on the balanced loss function and the maximum entropy optimization,the credibility premium is estimated.Finally,the numerical simulation shows that this method is better than the classical reliability estimation.