Abstract
In this paper, we study the representation for weighted average Value at Risk(WVaR) with respect to a capacity. We show that the WVaR with respect to a capacity can be represented as Choquet integral with respect to a corresponding distorted capacity, and for a submodular capacity with continuity from above, the WVaR can be characterized as the maximum value of a family of linear expectations. Moreover, we introduce a special kind of WVaR with respect to a capacity.
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