Abstract We study a generalized risk process , where Y is a Lévy process, C an independent subordinator and τ an independent exponential time. Dropping the standard assumptions on the finite expectations of the processes Y and C and the net profit condition, we derive a Pollaczek–Khinchine type formula for the supremum of the dual process on which generalizes previously known results. We also discuss which assumptions are necessary for deriving this formula, especially from the point of view of the ladder process.

中文翻译：

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广义风险过程的suprema分布

摘要 我们研究了广义风险过程 ，其中 Y 是 Lévy 过程，C 是独立的从属函数，τ 是独立的指数时间。去掉对过程 Y 和 C 的有限预期以及净利润条件的标准假设，我们推导出了一个 Pollaczek-Khinchine 型公式，用于对先前已知结果进行概括的对偶过程的上限值。我们还讨论了推导出这个公式需要哪些假设，特别是从阶梯过程的角度来看。