Robust optimized certainty equivalents and quantiles for loss positions with distribution uncertainty

Paper: arXiv 2304.04396

Authors: Weiwei Li, Dejian Tian

Abstract

The paper investigates the robust optimized certainty equivalents and analyzes the relevant properties of them as risk measures for loss positions with distribution uncertainty. On this basis, the robust generalized quantiles are proposed and discussed. The robust expectiles with two specific penalization functions $\varphi_{1}$ and $\varphi_{2}$ are further considered respectively. The robust expectiles with $\varphi_{1}$ are proved to be coherent risk measures, and the dual representation theorems are established. In addition, the effect of penalization functions on the robust expectiles and its comparison with expectiles are examined and simulated numerically.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a highly rigorous theoretical framework focused on robust optimized certainty equivalents, expectiles, and distribution uncertainty with dual representation theorems. However, it lacks extensive empirical backtesting on real-world market data, relying instead on limited numerical simulations.

Research Flowchart

  flowchart TD
    A[Research Goal: Formulate & analyze robust OCEs<br>and quantiles under distribution uncertainty] --> B[Inputs: Loss positions, uncertainty sets,<br>& penalization functions φ1, φ2]
    B --> C[Methodology: Derive robust generalized quantiles<br>& study robust expectiles]
    C --> D[Computational/Numerical Analysis:<br>Simulate penalization effects vs. standard expectiles]
    D --> E[Outcome 1: Robust φ1-expectiles proved<br>as coherent risk measures]
    D --> F[Outcome 2: Established dual representation theorems<br>& quantified penalization impact]