Representation theorems for WVaR with respect to a capacity

Hongmin Yuan, Long Jiang and Dejian Tian

Statistics & Probability Letters, 2020, vol. 158, issue C

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.

Keywords: WVaR; AVaR; Capacity; Distorted capacity; Choquet integral; Representation (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2019.108655

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