Minimum Cross-Entropy Transform of Risk Analysis

Transform is an important method of risk analysis in actuarial science. In this paper, a new transform method is proposed by the minimum cross-entropy principle which is used widely in information theory. The more moment information of loss variable can be considered in the bounds of the optimization model. The solution of the constructed model,which is a transform of original probability distribution,can be obtained easily by the way of Lagrange parameter. The essence of risk shift is indicated by distributing more weight to unfavorable events. The study shows that the new minimum cross-entropy transform (MCET) is correlated closely to Esscher transform. The relationship between them is also established here.