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arXiv · 2402.18014

Set-valued Star-Shaped Risk Measures

Bingchu Nie·Dejian Tian·Long Jiang
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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.

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Bingchu Nie, Dejian Tian, Long Jiang. 2024-02-28. Set-valued Star-Shaped Risk Measures. https://arxiv.org/abs/2402.18014

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