Best- and worst-case Scenarios for GlueVaR distortion risk measure with Incomplete information

TL;DR

This paper develops a unified framework to determine the best- and worst-case scenarios for the GlueVaR distortion risk measure under incomplete distribution information, including shape constraints like symmetry.

Contribution

It introduces a method to characterize extremal distributions of GlueVaR, encompassing VaR, TVaR, and RVaR, with convex envelopes of distortion functions.

Findings

Derived extremal distributions for GlueVaR under partial info

Characterized extremal cases for VaR, TVaR, RVaR

Provided a unified approach for risk measure bounds

Abstract

This paper derives the best- and worst-case GlueVaR distortion risk measure within a unified framework, based on partial information of the underlying distributions and shape information such as symmetry. In addition, we characterize the extremal distributions of GlueVaR with convex envelopes of the corresponding distortion functions. As examples, extremal cases of VaR, TVaR and RVaR are derived.