In the literature, some stochastic orders have been extended to the higher orders in different scenarios. In this paper, inspired by interesting properties of the excess wealth order and its wide range application particularly in comparing the tail variability of risks, we consider the second-order excess wealth order and study its main properties. We obtain two results characterizing the proposed order. We also investigate its relationship with other well-known variability orders and criteria to compare risks. An application of the results in comparing the epoch times of two nonhomogeneous poisson processes is also given.

中文翻译：

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二阶超额财富序及其性质

在文献中，一些随机阶已经扩展到不同场景中的更高阶。在本文中，受超额财富阶的有趣性质及其广泛应用的启发，特别是在比较风险的尾部变异性方面，我们考虑二阶超额财富阶并研究其主要性质。我们获得了两个表征提议顺序的结果。我们还调查了它与其他众所周知的可变性顺序和标准的关系，以比较风险。还给出了结果在比较两个非齐次泊松过程的纪元时间中的应用。