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

Content Provider	Springer Nature Link
Author	Gerber, Hans U. Shiu, Elias S. W. Yang, Hailiang
Copyright Year	2012
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.
Starting Page	259
Ending Page	272
Page Count	14
File Format	PDF
ISSN	21909733
Journal	European Actuarial Journal
Volume Number	2
Issue Number	2
e-ISSN	21909741
Language	English
Publisher	Springer-Verlag
Publisher Date	2012-07-31
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Omega model Discounted penalty Probability of bankruptcy Occupation times Airy functions Finance/Investment/Banking Game Theory, Economics, Social and Behav. Sciences Applications of Mathematics Quantitative Finance
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Economics and Econometrics Statistics, Probability and Uncertainty

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