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Representation theorems for WVaR with respect to a capacity

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  • Yuan, Hongmin
  • Jiang, Long
  • Tian, Dejian

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.

Suggested Citation

  • Yuan, Hongmin & Jiang, Long & Tian, Dejian, 2020. "Representation theorems for WVaR with respect to a capacity," Statistics & Probability Letters, Elsevier, vol. 158(C).
    • Handle: RePEc:eee:stapro:v:158:y:2020:i:c:s0167715219303013
    DOI: 10.1016/j.spl.2019.108655
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    References listed on IDEAS

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    1. Montes, Ignacio & Salamanca, Juan Jesús & Montes, Susana, 2020. "A modified version of stochastic dominance involving dependence," Statistics & Probability Letters, Elsevier, vol. 165(C).

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