Paper: arXiv 2503.15824

Authors: Yuxin Du, Dejian Tian, Hui Zhang

Abstract

The paper investigates the robust distortion risk measure with linear penalty function under distribution uncertainty. The distribution uncertainties are characterized by predetermined moment conditions or constraints on the Wasserstein distance. The optimal quantile distribution and the optimal value function are explicitly characterized. Our results partially extend the results of Bernard, Pesenti and Vanduffel (2024) and Li (2018) to robust distortion risk measures with linear penalty. In addition, we also discuss the influence of the penalty parameter on the optimal solution.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents rigorous mathematical proofs and explicit closed-form characterizations for robust distortion risk measures with a linear penalty term under Wasserstein distribution uncertainty. However, it is entirely theoretical with minimal empirical validation or backtesting on real-world financial market data.

Research Flowchart

  flowchart TD
    A[Research Goal: Compute Robust Distortion Risk Measures with Linear Penalty under Uncertainty] --> B[Inputs: Distortion Function, Linear Penalty Parameter & Reference Distribution]
    B --> C[Model Distribution Uncertainty: Moment Constraints & Wasserstein Distance]
    C --> D[Methodology: Quantile Optimization & Dual Reformulation]
    D --> E[Key Outcomes: Explicit Optimal Quantile Distribution & Optimal Value Function]
    E --> F[Analysis: Penalty Parameter Effects & Extension of Bernard et al. 2024 / Li 2018]

Cited References (24)

  1. An extreme worst-case risk measure by expectile (2024) — link
  2. Portfolio Optimization within a Wasserstein Ball (2023) — link
  3. Robust distortion risk measures (2022) — link
  4. Cash-Subadditive Risk Measures Without Quasi-Convexity (2021) — link
  5. Optimizing distortion riskmetrics with distributional uncertainty (2020) — link
  6. Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances (2018) — link
  7. Computational aspects of robust optimized certainty equivalents and option pricing (2017) — link
  8. Distributionally Robust Stochastic Optimization with Wasserstein Distance (2016) — link
and 16 more
  1. Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations (2015) — link
  2. Quasiconvex risk statistics with scenario analysis (2015) — link
  3. Robust risk measurement and model risk (2014) — link
  4. Remarks on quantiles and distortion risk measures (2012) — link
  5. Risk measures with comonotonic subadditivity or convexity and respecting stochastic orders (2009) — link
  6. Convex measures of risk and trading constraints (2002) — link
  7. Coherent Measures of Risk (1999) — link
  8. Axiomatic characterization of insurance prices (1997) — link
  9. Premium Calculation by Transforming the Layer Premium Density (1996) — link
  10. Distributionally Robust Optimization under Distorted Expectations (2020) — link
  11. Technical Note - Closed-Form Solutions for Worst-Case Law Invariant Risk Measures with Application to Robust Portfolio Optimization (2018)
  12. Optimal transport: old and new (Vol. 338, p. 23) (2009)
  13. Spectral Measures of Risk : a Coherent Representation of Subjective Risk Aversion (2002)
  14. Stochastic Finance: An Introduction in Discrete Time (2002)
  15. The Dual Theory of Choice under Risk (1987) — link
  16. Coming back to (4.2), one recognizes that ˆ G − 1 δ is the optimal quantile function. Noting that ˆ σ 0 > 0, we can easily get ˆ σ δ > 0 for all δ ≥ 0. Furthermore

0 of 24 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.