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Journal of Applied Mathematics and Stochastic Analysis
Volume 2004 (2004), Issue 3, Pages 221-234
http://dx.doi.org/10.1155/S1048953304309032

The Pólya-Aeppli process and ruin problems

Faculty of Mathematics and Informatics, Sofia University “St. Kliment Ohridski” , 5 James Bourchier Boulevard, Sofia 1164, Bulgaria

Received 16 September 2003; Revised 21 May 2004

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The Pólya-Aeppli process as a generalization of the homogeneous Poisson process is defined. We consider the risk model in which the counting process is the Pólya-Aeppli process. It is called a Pólya-Aeppli risk model. The problem of finding the ruin probability and the Cramér-Lundberg approximation is studied. The Cramér condition and the Lundberg exponent are defined. Finally, the comparison between the Pélya-Aeppli risk model and the corresponding classical risk model is given.