The Omega-model with two bankruptcy rates

The Omega model assumes that the company continues to do business even when the surplus is negative. However, when the surplus is negative, the bankruptcy probability increases when the deficit grows. We study the Omega model with two state dependent bankruptcy rates, where bankruptcy occurs with probability 1 when the surplus is below a given negative level. Both the classical Cramér-Lundberg risk model and the dual risk model are considered. We obtain the Laplace transforms of the time until bankruptcy and of the time that the surplus is negative.