Paper: arXiv 2405.19075

Authors: Baishuai Zuo, Chuancun Yin

Abstract

In this paper, we discuss the worst-case of distortion riskmetrics for general distributions when only partial information (mean and variance) is known. This result is applicable to general class of distortion risk measures and variability measures. Furthermore, we also consider worst-case of weighted entropy for general distributions when only partial information is available. Specifically, we provide some applications for entropies, weighted entropies and risk measures. The commonly used entropies include Gini functional, cumulative residual entropy, tail-Gini functional, cumulative Tsallis past entropy, extended Gini coefficient and so on. The risk measures contain some premium principles and shortfalls based on entropy. The shortfalls include the Gini shortfall, extended Gini shortfall, shortfall of cumulative residual entropy and shortfall of cumulative residual Tsallis entropy with order $α$.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides rigorous mathematical proofs establishing worst-case bounds for distortion riskmetrics and weighted entropy under partial moment information. However, it is entirely theoretical with minimal empirical validation or backtesting on real-world financial data.

Research Flowchart

  flowchart TD
    A[Research Goal: Worst-cases of Distortion Riskmetrics & Weighted Entropy under Partial Info] --> B[Inputs: Mean and Variance Information Only]
    B --> C[Methodology: Optimization under Partial Information Constraints]
    C --> D[Compute Worst-Case Bounds for Distortion Riskmetrics & Weighted Entropy]
    D --> E[Apply to Specific Entropies: Gini, Cumulative Residual, & Tsallis]
    D --> F[Apply to Risk Measures: Premium Principles & Entropy-based Shortfalls]
    E --> G[Outcomes: Unified Framework for Tail Risk Evaluation & Robust Risk Management]
    F --> G

Cited References (43)

  1. Extremal cases of distortion risk measures with partial information — → 2404.13637
  2. A family of variability measures based on the cumulative residual entropy and distortion functions (2023) — link
  3. Covariance Representations and Coherent Measures for Some Entropies (2023) — link
  4. Distortion risk measure under parametric ambiguity (2023) — link
  5. On weighted cumulative Tsallis residual and past entropy measures (2021) — link
  6. Fractional generalized cumulative entropy and its dynamic version (2021) — link
  7. On a family of coherent measures of variability (2020) — link
  8. DISTORTION RISKMETRICS ON GENERAL SPACES (2020) — link
and 35 more
  1. Characterization, Robustness, and Aggregation of Signed Choquet Integrals (2020) — link
  2. Range Value-at-Risk bounds for unimodal distributions under partial information (2020) — link
  3. Convex risk functionals: Representation and applications (2020) — link
  4. Fractional cumulative residual entropy (2019) — link
  5. Some properties of cumulative Tsallis entropy of order $$\alpha $$α (2019) — link
  6. On a family of risk measures based on proportional hazards models and tail probabilities (2019) — link
  7. PROPERTIES FOR GENERALIZED CUMULATIVE PAST MEASURES OF INFORMATION (2018) — link
  8. Worst-Case Range Value-at-Risk with Partial Information (2018) — link
  9. Some properties of cumulative Tsallis entropy (2017) — link
  10. Some Results on Weighted Cumulative Entropy (2017)
  11. Gini-Type Measures of Risk and Variability: Gini Shortfall, Capital Allocations, and Heavy-Tailed Risks (2017) — link
  12. Extended Gini-Type Measures of Risk and Variability (2017) — link
  13. On weighted cumulative residual entropy (2017) — link
  14. ON GENERALIZED CUMULATIVE ENTROPIES (2016) — link
  15. Weighted cumulative entropies: An extension of CRE and CE (2015) — link
  16. Generalized cumulative residual entropy and record values (2013) — link
  17. Remarks on quantiles and distortion risk measures (2012) — link
  18. Weighted cumulative entropy and its estimation (2011) — link
  19. Tight Bounds for Some Risk Measures, with Applications to Robust Portfolio Selection (2011) — link
  20. Entropy, longevity and the cost of annuities (2011) — link
  21. Convex optimization (2010) — link
  22. On cumulative entropies (2009) — link
  23. Cumulative residual entropy: a new measure of information (2004) — link
  24. Worst-Case Value-At-Risk and Robust Portfolio Optimization: A Conic Programming Approach (2003) — link
  25. A CLASS OF DISTORTION OPERATORS FOR PRICING FINANCIAL AND INSURANCE RISKS (2000) — link
  26. Premium Calculation: Why Standard Deviation Should be Replaced by Absolute Deviation (1990) — link
  27. Handbook of Mathematical Functions with Formulas (1965) — link
  28. A MODIFICATION OF SCHWARZ’S INEQUALITY WITH APPLICATIONS TO DISTRIBUTIONS’ (1953) — link
  29. Distributionally Robust Optimization under Distorted Expectations (2020) — link
  30. Closed-Form Solutions for Extreme-Case Distortion Risk Measures and Applications to Robust Portfolio Management (2018) — link
  31. Some new results on the cumulative residual entropy (2010) — link
  32. Actuarial Theory for Dependent Risks (2005)
  33. Classical and New Inequahties and Analysis (1993)
  34. The Dual Theory of Choice under Risk (1987) — link
    1. Bounds for Gini’s mean di ff erence based on first four moments, with some applications

1 of 43 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.