The Study About The Credibility Models Under Several Kinds Of Loss Functions

Credibility theory is a rate premium tool,which is based on historical empirical data of individual risk and a policy portfolio risk to determine the future premiums.In the classical credibility,the literature usually assume that claims data follow a particular distribution,and use symmetric loss function as the evaluation criterion,all claims have the same weight in the classical credibility theory.However,these assumptions are clearly not reasonable in practice.The main work of this paper is to study the credibility premium and exact credibility under various structural distributions,and deduce formulas of Bayes premium and credibility premium by using Mlinex loss function.In the case of unknown about distributions of the claims data,this paper adopts the maximum entropy method to optimize the credibility formula,it is concluded that claims in different years have different weights.In addition,the article utilizes credibility theory to predict wind speed in wind farm,and the forecast results are accurate and effective.The detailed content of this paper includes the following sections:The first chapter,we briefly introduce various structural distributions,asymmetric loss functions and the maximum entropy method of this paper,the current research at home and abroad and the main content of credibility premium.The second chapter,the basic knowledge of PH distribution in our paper are introduced,and deduce the credibility premium with inflation factor and the balanced loss function.The third chapter,based on the Mlinex loss function,we obtain Bayes premium,credibility premium and credibility formula by the maximum entropy method.The fourth chapter,we apply the thought of classical credibility premium to the wind power forecasting.The fifth chapter,the main result of this paper is summarized and the further research in the future is proposed.