The Credibility Estimation Based On Esscher Premium Principle

The classic reliability premiums are based on the quadratic loss function.The premiums received are called pure premiums.However,in insurance practice,pre-miums collected by insurance companies cannot be pure premiums and must meet,positive safety loads.In order to solve this problem,scholars proposed two solution-s.One is to add a safety factor to the net premium;the other is to choose other loss function that is different from the square loss,corresponding to In the ground,different loss functions correspond to different premium calculation principles.The main work of this paper is to study the reliability of Esscher premiums and the consistency of their premiums under the principle of premium,and to derive the reliability of Esscher premiums under the balance loss function.When the distribution of claims data is unknown,t,he maximum entropy method is used to calculate.The reliability formula yields the conclusion that historical claim amounts in different years have different weights.The specific content includes the following sections:The first chapter,paper briefly discusses Esscher's premium principle,balance loss function,the research significance of estimating trust premium based on the maximum entropy method,domestic and foreign research overview and research methods.The second chapter,This paper briefly introduces the theoretical knowledge of Esscher's premium principle,and gives a,consistent reliability premium by adopting the least square method under the principle of premium.The third chapter,Based on the principle of Esscher premium,the expression of reliability premium is derived under the equilibrium loss function.The fourth chapter,Using the maximum entropy method,Esscher reliability premium based on Esscher premium principle is obtained.This method is a further amendment to the classic reliability premium,optimizing the original reliability expression form,thus popularizing the classical Esscher letter.Premiums.The fifth chapter,Summarize the main research result,s in this paper,and put,forward questions that need further study in the future.