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- Publisher
- Wiley
- Copyright
- Copyright © 2008 John Wiley & Sons, Ltd.
- ISSN
- 1524-1904
- eISSN
- 1526-4025
- DOI
- 10.1002/asmb.752
- Publisher site
- See Article on Publisher Site
Abstract
In this paper, we consider a renewal risk process with random premium income based on a Poisson process. Generating function for the discounted penalty function is obtained. We show that the discounted penalty function satisfies a defective renewal equation and the corresponding explicit expression can be obtained via a compound geometric tail. Finally, we consider the Laplace transform of the time to ruin, and derive the closed‐form expression for it when the claims have a discrete Km distribution (i.e. the generating function of the distribution function is a ratio of two polynomials of order m∈ℕ+). Copyright © 2008 John Wiley & Sons, Ltd.
Journal
Applied Stochastic Models in Business and Industry – Wiley
Published: Nov 1, 2009