Department of Mathematics
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. © 2008 Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag GmbH.
Absolutely continuous, Aggregate claim distribution, Collective risk model, Compound distribution, Recursive algorithm
Source Publication Title
Acta Mathematicae Applicatae Sinica
Chinese Mathematical Society
Link to Publisher's Edition
Wang, Rong-Ming, Kam C. Yuen, and Li-Xing Zhu. "On the distributions of two classes of multiple dependent aggregate claims." Acta Mathematicae Applicatae Sinica 24.4 (2008): 655-668.