# 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

Fund

Title

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

Journal

European Actuarial Journal

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

Create date

11/12/2012 13:00

Last modification date

03/03/2018 17:06