Some Special Classes Of Dual Insurance Renewal Risk Model

The classical risk model is generalized in this text, the claim process is no longer a Poisson process but an ordinary renewal process and the delayed renewal process, and two kinds of claims could occur in one event, we discuss the models on the Gerber-Shiu discounted penalty function.Five chapters constitute this text.In the first chapter, we simply introduce the history, the present conditions of the risk theory and the main result, and we especially pay more attention on the classical risk model and its generalization. Finally we present the main content of this text and the main result of my research.In the second chapter, we outline the knowledge about expectation, point process, convolution and Laplace transform, and some theory on differential equation. This knowledge is also the foundation of the text.In the third chapter, we discuss an ordinary renewal risk model with two kinds of claims which could occur in one event, then get some results on the Gerber-Shiu discounted penalty function, ruin probability, surplus prior to ruin, deficit at ruin.In the fourth chapter, we change the model in chapter three to a delayed renewal risk model, get some relationships between these two models on the Gerber-Shiu discounted penalty function and ruin probability using Laplace transforms.In the fifth chapter, we put the interest on the two renewal models in the third and fourth chapter, and then get some results.