A Correlated With Threshold Dividend Strategy At Risk Model Gerber-Shiu Discounted Penalty Function

This dissertation is devoted to study the Gerber-Shiu discounted penalty function of a risk model with Double-type-insurance and constant dividend barrier.From the Lundberg-Cramer classical risk model is introduced, many scholars have promoted and improved it to adapt to the actual operations of the insurance company further. Today there are dozens of different types of risk model. With the development of the domestic insurance industry and the increasingly fierce competition in the insurance market, the multitype-insurance business has become the mainstream business in the insurance companies. And many types of insurance are interdependent and interrelated, so the research of the risk model with related insurance is very important and promising.This dissertation briefly describes the history of the evolution of the risk model and the main results. A risk model with Double-type-insurance and constant dividend barrier is established on the basis of previous work. This dissertation studies some properties of the Gerber-Shiu discounted penalty function. The integro-differential equations and the renewal equations are obtained. The explicit expression is given for Ψ(0).