不完全信息下损失风险的研究

在获得损失分布不完全信息情况下,提出用方差和熵共同度量损失风险的方法.在不完全信息条件下,通过最大熵原理在最不确定的情况下得到最大熵损失分布,并获得了损失分布的熵函数值.用熵值度量损失分布对于均匀分布的离散程度,从而度量概率波动带来的风险;用方差度量损失对于均值的离散程度,从而度量状态波动带来的风险.由于熵是与损失变量更高阶矩信息相联系的,所以新方法是从更全面的角度对损失风险的预测.通过算例,进一步看出在获得高阶矩信息下,熵参与风险度量的必要性.

Research on Loss Risk under Incomplete Information

This paper presents a new risk measure which combines variance and entropy under the incomplete information of the loss distribution.The estimate of maximum entropy loss distribution and the value of entropy function are obtained by the maximum entropy principle.The entropy and variance measure the disparity of loss distribution from the uniform one and the disparity of practical loss from the mean value respectively.Thus,the entropy and variance are used to measure fluctuant probability risk and state risk.This new method is more comprehensive forecast for loss risk because entropy is relative to more moment information.Further,the necessary of entropy measure risk is embodied by an example.