Asymptotic results on tail moment for light-tailed risks

Abstract

In this paper, we focus on the asymptotic behavior of a recently popular risk measure called the tail moment (TM), which has been extensively applied in the field of risk theory. We conduct the study under the framework in which the individual risks of a financial or insurance system follow convolution equivalent or Gamma-like distributions. Precise asymptotic results are obtained for the TM when the individual risks are mutually independent or have a dependence structure of the Farlie-Gumbel-Morgenstern type. Moreover, based on some specific scenarios, we give an asymptotic analysis on the relative errors between our asymptotic results and the corresponding exact values. Since the model settings in this paper are not covered by traditional ones, our work fills in some gaps of the asymptotic study of the TM for light-tailed risks.