On the Distributions of Two Classes of Multiple Dependent Aggregate Claims

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.

On the distributions of two classes of multiple dependent aggregate claims

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. The first author’s work was partially supported by a grant the from National Natural Science Foundation of China (10671072), by the Doctoral Program Foundation of the Ministry of Education of China (20060269016) and by the National Basic Research Program of China (973 Program, 2007CB814904). The second and third authors’ work were by grants from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No:HKU 7139/01H, 7323/01M, 7054/04P and 7060/04P).