Second-order asymptotics of the risk concentration of a portfolio with deflated risks (Q1720948)

Summary: The quantification of diversification benefits due to risk aggregation has received more attention in the recent literature. In this paper, we establish second-order asymptotics of the risk concentration based on several risk measures for a portfolio of \(n\) identically distributed but dependent deflated risks \(X_j = R_j S\), \(j = 1,2, \ldots, n\) under the assumptions of second-order regular variation on the survival functions of the risks \(R_j\) and the deflator \(S\), where \(R_1, R_2, \ldots, R_n\) are \(n\) independent and identically distributed random variables with a common survival function and \(S\) is a random variable being independent of \(R_1, R_2, \ldots, R_n\). Examples are also given to illustrate our main results.