In this work, we provide robust bounds on the tail probabilities and the tail index of heavy-tailed distributions in the context of model misspecification. They are defined as the optimal value when computing the worst-case tail behavior over all models within some neighborhood of the reference model. The choice of the discrepancy between the models used to build this neighborhood plays a crucial role in assessing the size of the asymptotic bounds. We evaluate the robust tail behavior in ambiguity sets based on the Wasserstein distance and Csisz\'ar $f$-divergence and obtain explicit expressions for the corresponding asymptotic bounds. In an application to Danish fire insurance claims we compare the difference between these bounds and show the importance of the choice of discrepancy measure.

翻译：在这项工作中,我们在模型误差的背景下,提供了尾部概率和重尾尾尾部分布的尾部指数的严格界限。 它们被定义为在计算参考模型某些周边所有模型中最坏的尾部行为时的最佳价值。 选择用于建造这个街区的模型之间的差异在评估无药可依界限的大小方面起着关键作用。 我们根据瓦西尔斯坦距离和Csisz\'ar $f$ar-diverence 来评估含混的尾部行为,并获得相应的无药可耐界限的明确表达。 在丹麦消防保险的应用程序中,我们比较了这些界限之间的差异,并表明了选择差异计量的重要性。