Abstract
Ruin ensues for the first time when a company's surplus is negative. The Omega model assumes that even with a negative surplus, the corporation can continue to operate normally until bankruptcy happens. The bankruptcy probability at a given point in time is solely determined by the value of the negative surplus at that point in time. The estimated discounted value of a penalty at bankruptcy, and thus the probability of bankruptcy, is determined under the assumption of Brownian motion for the surplus. There is an inherent relationship between the likelihood of not filing for bankruptcy and an exposure random variable. This minor dissertation investigates the time that an institution can operate at negative initial surplus until regulators deem it bankrupt, and the time of default. This is done by studying how long the surplus remains negative until bankruptcy occurs, using the Omega model. This thesis investigates the probability of bankruptcy at constant rates, and rates lower and/or higher than the initial surplus. The time in which ruin occurs is investigated using the Laplace transform. Findings show that an increase in the adjustment coefficient increases the probability of ruin.
Keywords: Omega model, Discounted penalty, Probability of bankruptcy, Ruin theory.