On the second-order excess wealth order and its properties

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.