Distortion risk measures: Prudence, coherence, and the expected shortfall
Bibliographic record
Abstract
Abstract Distortion risk measures (DRM) are risk measures that are law invariant and comonotonic additive. The present paper is an extensive inquiry into this class of risk measures in light of new ideas such as qualitative robustness, prudence and no reward for concentration, and tail relevance. Results include several characterizations of prudent DRMs, a novel representation of coherent DRMs as well as an axiomatization of the Expected Shortfall alternative to the one recently provided by Wang and Zitikis. By linking the two axiomatizations, the paper provides a new perspective on the idea of no reward for concentration. The paper also contains results of independent interest such as the lower semicontinuity with respect to convergence in distribution of the Haezendonck–Goovaerts risk measures, the extension of non‐necessarily convex risk measures as well as the structure of the core of a general submodular distortion.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.013 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.004 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".