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

Paper: arXiv 2409.19902

Authors: Mengshuo Zhao, Chuancun Yin

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.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides rigorous mathematical derivations for closed-form best- and worst-case bounds for the GlueVaR risk measure under moment and symmetry constraints. However, it is purely theoretical with zero empirical data or backtesting analysis included in the provided text.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Derive Best- & Worst-Case GlueVaR<br>under Incomplete Information"] --> B["Inputs:<br>Partial Distribution Info<br>& Shape Constraints (e.g., Symmetry)"]
    B --> C["Methodology:<br>Construct Convex Envelopes<br>of Distortion Functions"]
    C --> D["Process:<br>Unify Framework to Characterize<br>Extremal Distributions"]
    D --> E["Outcomes:<br>Exact GlueVaR Bounds & Extremal Cases<br>for VaR, TVaR, and RVaR"]