In Multi-stage Dividend Dependent Risk Model For The Gerber-shiu Function

A dependent risk model between claim sizes and interclaim arrivals was proposed by Boudreault,et al in 2006.About the compound Poisson risk model with a threshold dividend strategy,it can be found in Lin X.S.,Pavlova, K.P.(2006).The compound Poisson risk model with multiple thresholds is can be found in Lin X.S.,Kristina P.Sendova(2008).The aim of this thesis is to derive the Gerber-Shiu discounted penalty function of the dependent risk model between interclaim arrivals and claim sizes with two threshold dividend strategies and gets the results as follows:one is its integro-differential equations satisfied by the Gerber-Shiu discounted penalty function.Two is to do a further research and gets the defective renewal equations of m₃(u).Three is to expand the model and gets a general formula of n + 1 parts divided.The thesis is divided into four chapters according to contents:Chapter 1 is mainly to introduce the development process of risk model from the independent model to the dependent model.The research of the risk model given bonus mostly through such a process:firstly,the independent risk model there is no boundary,secondly there is one boundary,last is more than two boundaries.For the dependent risk model is also to follow this a basic process.In Chapter 2,we mainly derive the integro-differential equations satisfied by the Gerber-Shiu discounted penalty function for the dependent risk model in Sections 1-4.In Section 5,letδ= 0 and letδ= 0,b₂â†'∞,and get two special results.One is the Gerber-Shiu discounted penalty function of the compound Poisson risk model with multiple thresholds,two is the Gerber-Shiu discounted penalty function of the compound Poisson risk model with a threshold dividend strategy.In Chapter 3,the defective renewal equation satisfied by m₃(u)is got further research.First the renewal equation of m₃(u)is got,then is to prove that it is a defective renewal equation.In Chapter 4,is to further expand the three parts model to n+1 parts model. A basic conclusion of equations satisfied by Gerber-Shiu discounted penalty function was got in the end.