Set-Valued Weighted Value at Risk and Its Computation

摘要

In this paper, we propose a new class of set-valued coherent risk measures called the set-valued weighted value at risk. Firstly, the “regulator” version is independent of other market scenarios. The second version, which is called the market extension, is related to different market scenarios. The proofs of the properties of both versions are given, and equivalent representations are provided that enable us to compute the values of both versions of set-valued weighted value at risk. Finally, we offer examples to illustrate various features of the theoretical constructions of the set-valued weighted value at risk.Mathematics Subject Classification (2010): 91B30 91B32 91B70.