Abstract
In this paper, we study the asymptotic behavior of three types of Marginal Expected Shortfalls with different reference indices of the overall risk. Our results for the asymptotic independence case are obtained under quite general frameworks, in which no specific distribution class of each individual risk is supposed. For the asymptotic dependence case, we conduct the study under two widely applied assumptions, which imply that the individual risks possess the Fréchet and Gumbel tails, respectively. We also give an analysis on the accuracy of our asymptotic results in various scenarios when there are two individual risks in the whole system.
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