Study On Some Problems Of Dual Risk Model

In most actuarial research papers, a compound Poisson model is often used to describe the aggregate claims of the surplus process. Recently dual risk model is studied by some researchers.This paper is devoted to studying the dual risk model. we mainly study the penalty function in continuous dual risk model and discrete dual risk model. Penalty function is one of the most important actuarial variables. In addition we study the discrete dual risk model. This paper is organized as follows:In section 1 and section 2, the risk theory were simply introdued about its background, main research results and the representative methods to deal with the problem. Then we mainly described the dual risk model.In section 3, we give the definition of penalty function in the dual risk model and we give the intergro-differential equation, and then we studied the Laplace transformation of the surplus before the last revene, and then we studied the penalty function in the mixture of exponential distributions.In section 4, we consider the penalty function and ruin probability in the dual risk model.