Paper: arXiv 2604.16438

Authors: Asmerilda Hitaj, Elisa Mastrogiacomo, Ilaria Peri, Marcelo Righi

Abstract

This paper develops an axiomatic framework for ranking metrics, a general class of functionals for evaluating and ordering financial or insurance positions. Unlike traditional risk-adjusted performance measures-such as the Sharpe ratio, RAROC, or Omega-that express reward per unit of risk, ranking metrics assign each position a performance level rather than a normalized return. Relying on monotonicity and a new property called cash-quasiconcavity, we derive representation results linking ranking metrics to families of acceptance sets and risk measures, extending the theory of acceptability indices. Classical ratios arise as special cases, while new examples-based on expected-loss, Lambda-quantile, and bibliometric indices-illustrate the framework’s flexibility. Empirical applications to portfolio ranking and climate-risk insurance demonstrate its practical relevance.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 4.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a strong theoretical and axiomatic foundation for ranking metrics, utilizing advanced functional analysis and representation theorems. However, its empirical validation is relatively light compared to its heavy mathematical machinery, placing it in the theoretical domain.

Research Flowchart

  flowchart TD
    A["Research Goal: Develop axiomatic framework<br>for ranking metrics beyond traditional ratios"] --> B["Key Axioms: Define Monotonicity &<br>Cash-Quasiconcavity properties"]
    B --> C["Mathematical Derivation: Link metrics to<br>acceptance sets & risk measure families"]
    D["Inputs: Financial portfolios &<br>Climate-risk insurance data"] --> E["Empirical Application: Evaluate expected-loss,<br>Lambda-quantile & bibliometric models"]
    C --> E
    E --> F["Outcomes: Unified ranking metric framework<br>extending acceptability indices"]

Cited References (25)

  1. Coherent measures of risk (1999)
  2. Gain, loss, and asset pricing (2000)
  3. Star-shaped risk measures (2022)
  4. New measures for performance evaluation (2009)
  5. Risk preferences and their robust representation (2013) — link
  6. Risk measures on P(R) and value at risk with probability/loss function (2014)
  7. Scientific research measures (2016)
  8. Convex measures of risk and trading constraints (2002)
and 17 more
  1. Cash-subadditive risk measures without quasi-convexity (2024) — link
  2. Quasi-convex Risk Measures and Acceptability Indices: Theory and Applications (2012)
  3. Star-shaped acceptability indexes (2024)
  4. Putting order in risk measures (2002)
  5. An index to quantify an individual’s scientific research output (2005)
  6. A new Hirsch-type index saves time and works equally well as the original h-index (2006)
  7. An axiomatic characterization of the Hirsch-index (2008)
  8. Generalizing the h-and g-indices (2008)
  9. Scientific research measures (2016)
  10. Putting order in risk measures (2002)
  11. Acceptability indexes via-expectations: an application to liquidity risk (2013)
  12. An axiomatization of $\Lambda$-quantiles (2022)
  13. Starshaped sets (2020)
  14. An introduction to omega (2002)
  15. RAROC at Bank of America: from theory to practice (1996)
  16. An axiomatization of $\Lambda$-quantiles (2022)
  17. Measuring risk with multiple eligible assets (2015)

0 of 25 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.