Research Of Credibility Theory And Regression Credibility Model

Many individual risk of many risks collection are non-homogeneous in real life, how to price each risk? When have both transcendental experience information and sample information, how to take full advantage of all the information, how to make optimal estimation; credibility theory is to solve the above problems.Bayesian estimation often has an absolute advantage on information utilization, because it takes full advantage of the complete information of the obtained data for each. This credibility estimate is Bayesian credibility. Bayesian credibility estimation often requires multiple integral and integral calculation process is too complicated to be operationalized. Same time, it often requires a probability distribution, but this information may not be obtained. It is due to the presence of such a problem, so Buhlmann (1967) first proposed using linear function approximation Bayesian estimation. Under certain assumptions, it greatly simplifies the computation. It came to the simple estimator. This estimator can be written in the form of credibility theory key equation, thereby establishing the modern theory of credibility theory.The second Section of this paper expounded the basic framework of the classical theory of credibility, and introduces the basic principle and the entirely credible conditions. It explores the defects and the causes of credibility theory in depth. The reason is not taken into account prior experience volatility. And it may lead credibility estimate into trap.Credibility theory modern is built on the basis of the theory of Bayesian estimation. Mainly take into account each individual in the overall distribution of the parameters are not necessarily identical. But, due to the Bayesian estimator are often too complex, and need to know a priori distribution function of the parameter space and in the posterior distribution function under the conditions of the given parameter, so have many other improved credibility estimates based on Bayesian estimation model. Chapter IV systematically explained the process and the principle of Bayesian credibility. Chapter IV, Section2describes the Buhlmann credibility. The Buhlmann credibility final form depends on only three parameters, without the need for prior distribution by assuming conditional distribution, in the form of simple conclusion image.Both the Buhlmann credibility Buhlmann-Straub credibility are built on the basis of i.i.d. But in Economic life, many panel data in the time dimension radiate a certain trend. The regression credibility model originated in the time trend data. Different from the traditional simple sample data, the regression credibility model takes into account the time trend and individual differences. The trend is reflected in the regression equation. In chapter VI, it describes the basic principles and methods of the regression model of credibility, and explores the iterative estimation method when residual autocorrelation. Finally, the example of the computer simulation results showed better results.