On the Probability and Severity of Ruin

Details

Serval ID
serval:BIB_454314BDCFF8
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
On the Probability and Severity of Ruin
Journal
ASTIN Bulletin
Author(s)
Gerber Hans U., Goovaerts Marc J., Kaas Rob
ISSN
0515-0361
1783-1350
Publication state
Published
Issued date
1987
Peer-reviewed
Oui
Volume
17
Number
02
Pages
151-163
Language
english
Abstract
In the usual model of the collective risk theory, we are interested in the severity of ruin, as well as its probability. As a quantitative measure, we propose G(u, y), the probability that for given initial surplus u ruin will occur and that the deficit at the time of ruin will be less than y, and the corresponding density g(u, y). First a general answer in terms of the transform is obtained. Then, assuming that the claim amount distribution is a combination of exponential distributions, we determine g; here the roots of the equation that defines the adjustment coefficient play a central role. An explicit answer is also given in the case in which all claims are of constant size.
Open Access
Yes
Create date
16/07/2018 15:45
Last modification date
21/08/2019 6:15
Usage data