Probability Risk Model of Claim Amount Affected by a Threshold Value

In this paper, we consider a new risk model of claim amount affected by a threshold value. The comparision between the claim interval and the threshold will affect the distribution of claims. The hypothesis of the model is presented and then we derive the roots of the Lundberg equation, and the expected discounted penalty function and its Laplace Transform. Besides, the Gerber- Shiu penalty function and some other functions are given when the initial surplus is zero and when they satifie some defective renewal equations. Some explicit expressions about the ruin probability are obtained too.