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

By Hans U. Gerber, E. Shiu, Hailiang Yang. 2012

61 citations recorded by the source corpus.

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.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/c6e2c387066873e4ea6d86d5048c512f1c60876d

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Citations in the corpus

The Joint Laplace Transforms for Diffusion Occupation Times (2013, background): “:3) e δ has been pointed out in [12].”
Occupation times of intervals until first passage times for spectrally negative Lévy processes (2012, methodology): “ Probability of bankruptcy for an Omega Lévy risk process. Our results can also be applied to the so-called Omega model (for some speciﬁc rate functions) introduced in [1] and further investigated in [4]. Intuitively in such a model bankruptcy (instead of ruin) occurs at rate ω(x) when the surplus p”