With Mixed Dividends For A Class Of Renewal Risk Model Of Bankruptcy

In this paper, we mainly study the Gerber-Shiu expectation discounted penalty func-tion in the Erlang(2) risk model with hybrid dividend strategy. The divided problem has become a research focus since the divided problem of the risk model was put forward. Lots of reference have generalised it. See Biihlmann (1970), Gerber (1972,1973,1981) for detail. In Gerber and Shiu (1998), Gerber and Shiu introduced a discounted penalty function to analyze these related quantities in a unified manner.Both barrier strategy and threshold strategy are important dividend strategies. In Lin and Willmot (2003), Lin and Willmot studied the compound Poisson risk model with a barrier dividend strategy. In Lin and Pavlova (2006), Lin and Pavlova studied the compound Poisson risk model with a threshold dividend strategy. Based on the above results, in this thesis, we study the Gerber-Shiu expectation discounted penalty function for Erlang(2) risk model and dependent Erlang(2) risk model respectively. We applied a strategy that the Barrier strategy combining with Threshold strategy.According to the contents, this dissertation is divided into three chapters:Chapter 1 is the introduction. In this part, the study situation and background of dividends payment problems is briefly introduced, which is prepared for the content of the next two chapters.Chapter 2, we have given the integro-differential equation of the Gerber-Shiu expec-tation discounted penalty function for Erlang(2) risk model, furthermore the mordel has been generalized into the generalized Erlang(n) risk model.Chapter 3, we have given the integre-differential equation of the Gerber-Shiu expec-tation discounted penalty function for dependent Erlang(2) risk model.