Second-Order Asymptotics of the Risk Concentration of a Portfolio with Deflated Risks

Abstract

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 Xj=RjS, j=1,2,…,n under the assumptions of second-order regular variation on the survival functions of the risks Rj and the deflator S, where R1,R2,…,Rn are n independent and identically distributed random variables with a common survival function and S is a random variable being independent of R1,R2,…,Rn. Examples are also given to illustrate our main results.