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Record W2965384330 · doi:10.1111/mafi.12270

Risk functionals with convex level sets

2020· article· en· W2965384330 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueMathematical Finance · 2020
Typearticle
Languageen
FieldDecision Sciences
TopicRisk and Portfolio Optimization
Canadian institutionsUniversity of Waterloo
FundersNatural Sciences and Engineering Research Council of CanadaSociety of Actuaries
KeywordsMathematicsIdentifiabilityQuantileDimension (graph theory)Coherent risk measureChoquet integralProperty (philosophy)Monotone polygonMeasure (data warehouse)Characterization (materials science)Class (philosophy)Risk measureRegular polygonMathematical economicsApplied mathematicsEconometricsPure mathematicsExpected shortfallRisk managementComputer scienceStatisticsEconomicsArtificial intelligenceFinance

Abstract

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Abstract We analyze the “convex level sets” (CxLS) property of risk functionals, which is a necessary condition for the notions of elicitability, identifiability, and backtestability, popular in the recent statistics and risk management literature. We put the CxLS property in the multidimensional setting, with a special focus on signed Choquet integrals, a class of risk functionals that are generally not monotone or convex. We obtain two main analytical results in dimension one and dimension two, by characterizing the CxLS property of all one‐dimensional signed Choquet integrals, and that of all two‐dimensional signed Choquet integrals with a quantile component. Using these results, we proceed to show that under some continuity assumption, a comonotonic‐additive coherent risk measure is co‐elicitable with Value‐at‐Risk if and only if it is the corresponding Expected Shortfall. The new findings generalize several results in the recent literature, and partially answer an open question on the characterization of multidimensional elicitability.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.002
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient payload (model declined to judge)
Consensus categoriesInsufficient payload (model declined to judge)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.818
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.002
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.001
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0010.003

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.

Opus teacher head0.172
GPT teacher head0.351
Teacher spread0.179 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it