Abstract

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.

中文翻译：

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具有两个破产率的 Omega 模型

摘要

Omega 模型假设即使盈余为负，公司仍会继续开展业务。然而，当盈余为负时，随着赤字的增加，破产概率增加。我们研究了具有两个状态相关破产率的 Omega 模型，其中当盈余低于给定的负水平时，破产发生的概率为 1。经典的 Cramér-Lundberg 风险模型和双重风险模型都被考虑在内。我们得到破产前时间和盈余为负时间的拉普拉斯变换。