The Boundary Values ​​of The Individual Risk Model, The Total Claim Amount Distribution Function Model To Promote Research

Research in the risk model is very important meaning in the theory and applications. From the facts of insurance , I found the new analyse ways which can be used to study the bounds of the claim amount distribution in individual risk models. In the basis of the bounds of portfolio we gained the ruin probability in this article. 1. When the claim amount distribution is some generic character, by the new analyse ways we can study the bounds of the claim amount distribution in individual risk models. In the basis of the bounds of portfolio we gained the ruin probability and others important targets. For example if one policy's claim distribution F(x) is increasing f(x)/F|-(x) with a finite mean μ(0<μ<∞),, then when 0≤x≤μ,F|-(x)≥e^-x/xμ) ; when x>μ,F|-(x)≥e^-x/xμ),1-ω=e^-x/xμ)where ω is 1-ω=e^-x/xμ) (0<ω<1)。Introducing the means which transform risk models with the different claim amount distribution to risk models with the same claim amount distribution. And I give some example of the transform in this chapter. And in the risk models with interest rate, discusses the important targets. 2. In open individual risk models, discusses the bounds of claim amount distribution in individual risk models by some characters of one policy's claim distribution. For example if one policy's claim distribution F(x) is E(X)=λ＜∞,Var(x)=σ²,and (?)x>0,1/λ(?)F|-(u)du≤F|-(x),thenp[1-F(x)]/[1-pF(x)]≤F|-s(x)≤pe^-λ(1-p)x-p(1-p)[M(x)-λx],And in the basis of the bounds of portfolio we gained the ruin probability.