Journal article
The Omega model: from bankruptcy to occupation times in the red
European Actuarial Journal, Vol.2(2), pp.259-272
12/2012
DOI: 10.1007/s13385-012-0052-6
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.
Details
- Title: Subtitle
- The Omega model: from bankruptcy to occupation times in the red
- Creators
- Hans Gerber - Department of Statistics and Actuarial Science The University of Hong Kong Pokfulam Road Hong Kong ChinaElias Shiu - Department of Statistics and Actuarial Science The University of Iowa Iowa City IA 52242-1409 USAHailiang Yang - Department of Statistics and Actuarial Science The University of Hong Kong Pokfulam Road Hong Kong China
- Resource Type
- Journal article
- Publication Details
- European Actuarial Journal, Vol.2(2), pp.259-272
- DOI
- 10.1007/s13385-012-0052-6
- ISSN
- 2190-9733
- eISSN
- 2190-9741
- Publisher
- Springer-Verlag; Berlin/Heidelberg
- Language
- English
- Date published
- 12/2012
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9983985931802771
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