Set-Valued Weighted Value at Risk and Its Computation

In this paper, we propose a new set-valued coherent risk measure called the set-valued weighted value at risk. The first "regulator" version is independent of any market model, whereas the second version, called the market extension, takes trading opportunities into account. Properties of both versions are proven, 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 a comparison with the existing set-valued average value at risk. Examples are provided to illustrate the theoretical construction of set-valued weighted value at risk.