Recursive Methods On Multiple Dependent Collective Risk Model

Collective Risk model is very important in actuary,and it is easy to handle in math-matics. But the calculation of total claim is a very complex problem in risk theory. Because usually we can't get the distribution of total claim directly.So it attracts many scholars's interests.Many scholars studied this problem and got some good results.Panjer put forward recursive method firstly. Recursive method is a very effective method for calculating total claim's probability distribution function in really.Recursive method is a hotspot in actuary since Panjer firstly put forward this method. Many famous scholars , such as Hessleager,O. and Gerber,H.U. and Panjer ,studied this method for more.Some get more extend in individual claim ,some got more extend in claim number ,and some studied the moment of total claim,and others studied the stability of calculation.In any cases ,the recursive can only hold in some conditions.The main purpose of this article is that we can use this nethod in more common casesIn this article,we study total claim's distribution in multidimensional dependent case.In charpter 2, we study contituous recursive method in multidimensional dependent case if the distribution of claim number is simple.In chaper 3,we extend Hesselager's(1994) and Wang & Sobrero's (1994) results to multidimensional dependent case.Especially we can get corresponding results in Sundt(1999) and Ambagaspitiya(1999).In chapter 4,we consider the claim numbers are dependent .In chapter 5, we study special case when the individual claim can be negative.This article gives two examples of calculation to show how to apply theroies of this article...