On the Distributions of Two Classes of Multiple Dependent Aggregate Claims  

作　　者：Rong-ming Wang Kam C. Yuen Li-xing Zhu 

机构地区：[1]School of Finance and Statistics, East China Normal University, Shanghai, 200241 China [2]Department of Statistics and Actuarial Science, The University of Hong Kong [3]Department of Mathematics, Hongkong Baptist University, Kowloon Tong, Hong Kong

出　　处：《Acta Mathematicae Applicatae Sinica》2008年第4期655-668,共14页应用数学学报（英文版）

基　　金：supported by a grant the from National Natural Science Foundation of China(10671072);the Doctoral Program Foundation of the Ministry of Education of China(20060269016);the National Basic Research Program of China(973 Program,2007CB814904);the Research Grants Council of the Hong Kong Special Administrative Region,China(Project No:HKU 7139/01H,7323/01M,7054/04P and 7060/04P).

摘　　要：In this paper we examine two classes of correlated aggregate claims distributions, with univariate claim counts and multivariate claim sizes. Firstly, we extend the results of Hesselager [ASTIN Bulletin, 24： 19-32（1994）] and Wang ＆ Sobrero＇s [ASTIN Bulletin, 24：161-166 （1994）] concerning recursions for compound distributions to a multivariate situation where each claim event generates a random vector. Then we give a multivariate continuous version of recursive algorithm for calculating a family of compound distribution. Especially, to some extent, we obtain a continuous version of the corresponding results in Sundt [ASTIN Bulletin, 29：29-45 （1999）] and Ambagaspitiya [Insurance： Mathematics and Economics, 24：301-308 （1999）]. Finally, we give an example and show how to use the algorithm for aggregate claim distribution of first class to compute recursively the compound distribution.In this paper we examine two classes of correlated aggregate claims distributions, with univariate claim counts and multivariate claim sizes. Firstly, we extend the results of Hesselager [ASTIN Bulletin, 24： 19-32（1994）] and Wang ＆ Sobrero＇s [ASTIN Bulletin, 24：161-166 （1994）] concerning recursions for compound distributions to a multivariate situation where each claim event generates a random vector. Then we give a multivariate continuous version of recursive algorithm for calculating a family of compound distribution. Especially, to some extent, we obtain a continuous version of the corresponding results in Sundt [ASTIN Bulletin, 29：29-45 （1999）] and Ambagaspitiya [Insurance： Mathematics and Economics, 24：301-308 （1999）]. Finally, we give an example and show how to use the algorithm for aggregate claim distribution of first class to compute recursively the compound distribution.

关 键 词：Compound distribution recursive algorithm collective risk model aggregate claim distribution absolutely continuous 

分 类 号：O1[理学—数学]