Some Random Variable's Approximation To The Individual Risk Model And Their Comparison

Individual risk model is one of the most basic risk models in Actuarial theory. The total compensation is the sum of all the individual compensations.Thus the risk can be measured by Laplace multiplication,but it is too complicated to get its exact answer,so we need another simpler methods.In this paper,it has to solve the problem,and find some other approximate methods,then compare them.There is main content of the paper below:1. In chapter 1,at first this paper reviews the central limit theorem.Then it takes two examples to compare the results and find it applicable range.But this kind of approximation is not satisfactory in insurance practice,the tail probability's error is obvious.So we need more exact approximation.We discuss the Gamma translation approximation and another NP approximation, then proves that it can modify the error of CLT.In this paper,in order to avoid complicated proof,it use excel diagrams in comparing their effects.2.In chapter2,this paper introduce another method to approximate S,that is Compound Poisson approximation.This approximation can also have many parameter choices,in this paper I choose two of the normal choices,and get the error upper limit.This method can avoid the "many" problem,but it is be effected by compensated probability.We can get the conclusion that different methods have different superiority and inferiority,we should choose the most suitable one.