标题： L{é}稳态过程轻尾跳跃的破产概率界分类 显示英文标题

标题： Classification of the Bounds on the Probability of Ruin for L{é}vy Processes with Light-tailed Jumps

摘要： 在本文中，我们研究了具有轻尾负跳跃的实值Lévy过程X的最终破产概率。众所周知，对于这样的Lévy过程，当初始值趋于无穷时，破产概率随着拉普拉斯指数根给出的指数函数而减少。在X具有可积正跳跃的附加假设下，我们展示了对拉普拉斯指数的更细致分析实际上给出了此类Lévy过程破产概率界限的完整描述。这导致识别出文献中未考虑的一种情况，并为此我们提供了一个例子。随后，我们将结果应用于各种风险模型，特别是由布朗运动扰动的Cramér-Lundberg模型。 显示英文摘要

摘要： In this note, we study the ultimate ruin probabilities of a real-valued L{\'e}vy process X with light-tailed negative jumps. It is well-known that, for such L{\'e}vy processes, the probability of ruin decreases as an exponential function with a rate given by the root of the Laplace exponent, when the initial value goes to infinity. Under the additional assumption that X has integrable positive jumps, we show how a finer analysis of the Laplace exponent gives in fact a complete description of the bounds on the probability of ruin for this class of L{\'e}vy processes. This leads to the identification of a case that is not considered in the literature and for which we give an example. We then apply the result to various risk models and in particular the Cram{\'e}r-Lundberg model perturbed by Brownian motion.