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G. Willmot, H. Panjer (1987)
Difference equation approaches in evaluation of compound distributionsInsurance Mathematics & Economics, 6
O. Hesselager (1994)
A Recursive Procedure for Calculation of some Compound DistributionsASTIN Bulletin, 24
H. Panjer, G. Willmot (1982)
Recursions for Compound DistributionsASTIN Bulletin, 13
H. Panjer (1981)
Recursive Evaluation of a Family of Compound DistributionsASTIN Bulletin, 12
B. Sundt, W. Jewell (1981)
Further Results on Recursive Evaluation of Compound DistributionsASTIN Bulletin, 12
T. Rolski (1999)
Stochastic Processes for Insurance and Finance
D. Antzoulakos, S. Chadjiconstantinidis (2004)
On Mixed and Compound Mixed Poisson DistributionsScandinavian Actuarial Journal, 2004
G.E. Willmot (1993)
On recursive evaluation of mixed Poisson probabilities and related quantitiest Scandinavian Actuarial Journal, 2
R. Ambagaspitiya (1999)
On the distributions of two classes of correlated aggregate claimsInsurance Mathematics & Economics, 24
Shaun Wang, Monica Sobrero (1994)
Further Results on Hesselager's Recursive Procedure for Calculation of some Compound DistributionsASTIN Bulletin, 24
B. Sundt (1999)
On Multivariate Panjer RecursionsASTIN Bulletin, 29
B. Sundt (1992)
On some Extensions of Panjer's Class of Counting DistributionsASTIN Bulletin, 22
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.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Oct 12, 2008
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