Paper: arXiv 2503.03471

Authors: Akif Ince, Marlon Moresco, Ilaria Peri, Silvana M. Pesenti

Abstract

We provide a constructive way of defining new elicitable risk measures that are characterised by a multiplicative scoring function. We show that depending on the choice of the scoring function’s components, the resulting risk measure possesses properties such as monotonicity, translation invariance, convexity, and positive homogeneity. Our framework encompasses the majority of well-known elicitable risk measures including all elicitable convex and coherent risk measures. Our setting moreover allows to construct novel elicitable risk measures that are, for example, convex but not coherent. Furthermore, we discuss how higher-order elicitability, such as jointly eliciting the mean and variance or different quantile levels, fall within our setting.

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 provides a rigorous mathematical foundation using Orlicz spaces to construct new classes of elicitable risk measures via multiplicative scoring functions. However, it is purely theoretical with no empirical backtests, real data applications, or provided code repository.

Research Flowchart

  flowchart TD
    A["Research Goal: Construct & characterize new elicitable risk measures"] --> B["Input: Multiplicative Scoring Functions & Component Choices"]
    B --> C["Methodology: Mathematical formulation of risk measures via scoring functions"]
    C --> D["Analysis: Evaluate properties (Monotonicity, Convexity, Coherence, Translation Invariance)"]
    D --> E["Extension: Generalize to Higher-Order Elicitability (e.g., Mean-Variance, Quantiles)"]
    E --> F["Outcomes: Unified framework covering known & novel convex/non-coherent risk measures"]

Cited References (31)

  1. Nonconvex extension of generalized huber loss for robust learning and pseudo-mode statistics (2022) — link
  2. Higher order elicitability and O sband’s principle (2016)
  3. Sensitivity measures based on scoring functions (2023)
  4. Making and Evaluating Point Forecasts (2011)
  5. Coherence and Elicitability (2016)
  6. Coherent measures of risk (1999)
  7. Back-testing E xpected S hortfall (2014)
  8. Elicitability and backtesting: Perspectives for banking regulation (2017)
and 23 more
  1. Putting order in risk measures (2002)
  2. Optimal transport divergences induced by scoring functions — → 2311.12183
  3. Risk Budgeting Allocation for Dynamic Risk Measures — → 2305.11319
  4. From proper scoring rules to max-min optimal forecast aggregation (2023)
  5. Scores for multivariate distributions and level sets (2023)
  6. Weighted scoring rules and convex risk measures (2022)
  7. On the measurement of economic tail risk (2016)
  8. Eliciting properties of probability distributions (2008)
  9. Risk contributions of L ambda quantiles (2022)
  10. Optimal rules and robust Bayes estimation of a Gamma scale parameter (2013)
  11. Elicitation and identification of properties (2014)
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  17. On the properties of the L ambda V alue at R isk: robustness, elicitability and consistency (2017)
  18. Lambda V alue at R isk and regulatory capital: a dynamic approach to tail risk (2018)
  19. An axiomatization of $\Lambda$-quantiles (2022)
  20. Convex measures of risk and trading constraints (2002)
  21. On elicitable risk measures (2015)
  22. Generalized Orlicz Spaces (2019)
  23. Functional equations and inequalities with applications (2009)

2 of 31 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.