The Omega model: from bankruptcy to occupation times in the red

Details

Serval ID
serval:BIB_4F61231721C9
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
The Omega model: from bankruptcy to occupation times in the red
Journal
European Actuarial Journal
Author(s)
Gerber H.U., Shiu E.S.W., Yang H.
ISSN
2190-9733
Publication state
Published
Issued date
12/2012
Peer-reviewed
Oui
Volume
2
Number
2
Pages
259-272
Language
english
Abstract
Ruin occurs the first time when the surplus of a company or an institution is negative. In the Omega model, it is assumed that even with a negative surplus, the company can do business as usual until bankruptcy occurs. The probability of bankruptcy at a point of time only depends on the value of the negative surplus at that time. Under the assumption of Brownian motion for the surplus, the expected discounted value of a penalty at bankruptcy is determined, and hence the probability of bankruptcy. There is an intrinsic relation between the probability of no bankruptcy and an exposure random variable. In special cases, the distribution of the total time the Brownian motion spends below zero is found, and the Laplace transform of the integral of the negative part of the Brownian motion is expressed in terms of the Airy function of the first kind.
Keywords
Omega model, discounted penalty, probability of bankruptcy, occupation times: airy functions
Open Access
Yes
Create date
11/12/2012 12:00
Last modification date
20/08/2019 14:05
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