As an important heavy tail distribution,subexponential distribution was widely used in finance and actuarial fields because of its ability to describe large claims.With the further development of risk model research,the second-order subexponential distribution was firstly proposed in 2008.Compared with the first-order subexponential distribution,its asymptotic expression was more accurate,so the research on the second-order subexponential distribution had attracted extensive attention in recent years.In this paper,the closure of the convolution and the convolution roots of second-order subexponential distribution were considered.First,the closure of second-order subexponential distribution on the family of second-order subexponential distribution under proportional equivalence was given,and then the convolution closure of second-order subexponential distribution was obtained.Finally,the conclusion about the closure of convolution roots was obtained.This paper expanded the research results of second-order subexponential distribution,which had important theoretical significance for future related research.
维普
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