Set-valued Star-Shaped Risk Measures

Bingchu Nie, Dejian Tian and Long Jiang

Papers from arXiv.org

Abstract: In this paper, we introduce a new class of set-valued risk measures, named set-valued star-shaped risk measures. Motivated by the results of scalar monetary and star-shaped risk measures, this paper investigates the representation theorems in the set-valued framework. It is demonstrated that set-valued risk measures can be represented as the union of a family of set-valued convex risk measures, and set-valued normalized star-shaped risk measures can be represented as the union of a family of set-valued normalized convex risk measures. The link between set-valued risk measures and set-valued star-shaped risk measures is also established.

Date: 2024-02, Revised 2025-02
New Economics Papers: this item is included in nep-rmg
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