Under contemporary insurance regulatory frameworks, an insolvent insurer placed in receivership may have the option of rehabilitation, during which a plan is devised to resolve the insurer's difficulties. The regulator and receiver must analyze the company's financial condition and determine whether a rehabilitation is likely to be successful or if its problems are so severe that the appropriate action is to liquidate the insurer. Therefore, it is essential to evaluate the cost required to support the insurer during its insolvent states in the decision-making process. To this end, we study areas in the red (below level 0) up to the recovery time, Poissonian, and continuous first passage times in this paper. Furthermore, we extend the study to the areas associated with Parisian ruin to evaluate the total cost until possible liquidation. For spectrally negative Lévy processes (SNLPs), also known as Lévy risk models, we derive the expectations of these quantities in terms of the well-known scale functions. Our results improve the existing literature, in which only expected areas for the Brownian motion and the Cramér-Lundberg risk process with exponential jumps are known.

在当代保险监管框架下，破产的保险公司被接管后可以选择重整，在此期间制定计划来解决保险公司的困难。监管机构和接管人必须分析公司的财务状况，并确定重组是否有可能成功，或者其问题是否严重到需要清算保险公司的适当行动。因此，有必要在决策过程中评估在保险公司处于资不抵债状态时支持其所需的成本。为此，我们研究了红色区域（0 级以下）直至恢复时间、泊松分布和本文中的连续首次通过时间。此外，我们将研究扩展到与巴黎废墟相关的区域，以评估在可能清算之前的总成本。对于光谱负 Lévy 过程 (SNLP)，也称为 Lévy 风险模型，我们根据众所周知的尺度函数推导出这些数量的期望值。我们的结果改进了现有文献，其中仅已知布朗运动的预期区域和具有指数跳跃的 Cramér-Lundberg 风险过程。