Set-valued Star-Shaped Risk Measures
Risk Management
2025-02-24 v2
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.
Keywords
Cite
@article{arxiv.2402.18014,
title = {Set-valued Star-Shaped Risk Measures},
author = {Bingchu Nie and Dejian Tian and Long Jiang},
journal= {arXiv preprint arXiv:2402.18014},
year = {2025}
}
Comments
26 pages, to appear in Mathematics and Financial Economics