PROPERTIES OF SECOND-ORDER REGULAR VARIATION AND EXPANSIONS FOR RISK CONCENTRATION

Abstract

The purpose of this study is two-fold. First, we investigate further properties of the second-order regular variation (2RV). These properties include the preservation properties of 2RV under the composition operation and the generalized inverse transform, among others. Second, we derive second-order expansions of the tail probabilities of convolutions of non-independent and identically distributed (i.i.d.) heavy-tail random variables, and establish second-order expansions of risk concentration under mild assumptions. The main results extend some ones in the literature from the i.i.d. case to non-i.i.d. case.