A direct approach to the discounted penalty function

Details

Ressource 1Download: BIB_34C00F94A9C8.P001.pdf (216.82 [Ko])
State: Public
Version: author
Serval ID
serval:BIB_34C00F94A9C8
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
A direct approach to the discounted penalty function
Journal
North American Actuarial Journal
Author(s)
Albrecher H., Gerber H.U., Yang H.
ISSN
1092-0277
Publication state
Published
Issued date
2010
Peer-reviewed
Oui
Volume
14
Number
4
Pages
420-434
Language
english
Abstract
This paper provides a new and accessible approach to establishing certain results concerning the discounted penalty function. The direct approach consists of two steps. In the first step, closed-form expressions are obtained in the special case in which the claim amount distribution is a combination of exponential distributions. A rational function is useful in this context. For the second step, one observes that the family of combinations of exponential distributions is dense. Hence, it suffices to reformulate the results of the first step to obtain general results. The surplus process has downward and upward jumps, modeled by two independent compound Poisson processes. If the distribution of the upward jumps is exponential, a series of new results can be obtained with ease. Subsequently, certain results of Gerber and Shiu [H. U. Gerber and E. S. W. Shiu, North American Actuarial Journal 2(1): 48–78 (1998)] can be reproduced. The two-step approach is also applied when an independent Wiener process is added to the surplus process. Certain results are related to Zhang et al. [Z. Zhang, H. Yang, and S. Li, Journal of Computational and Applied Mathematics 233: 1773–1 784 (2010)], which uses different methods.
Open Access
Yes
Create date
17/08/2010 14:07
Last modification date
20/08/2019 13:21
Usage data