Bibliographic record
Abstract
Coherent and convex risk measures, Choquet expectation and Peng’s g-expectation are all generalizations of mathematical expectation. All have been widely used to assess financial riskiness under uncertainty. In this paper, we investigate differences amongst these risk measures and expectations. For this purpose, we constrain our attention of coherent and convex risk measures, and Choquet expectation to the domain of g-expectation. Some differences among coherent and convex risk measures and Choquet expectations are accounted for in the framework of g-expectations. We show that in the family of convex risk measures, only coherent risk measures satisfy Jensen’s inequality. In mathematical finance, risk measures and Choquet expectations are typically used in the pricing of contingent claims over families of measures. The different risk measures will typically yield different pricing. In this paper, we show that the coherent pricing is always less than the corresponding Choquet pricing. This property and inequality fails in general when one uses pricing by convex risk measures. We also discuss the relation between static risk measure and dynamic risk measure in the framework of g-expectations. We show that if g-expectations yield coherent (convex) risk measures then the corresponding conditional g-expectations or equivalently the dynamic risk measure is also coherent (convex). To prove these results, we establish a new converse of the comparison theorem of g-expectations.
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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 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".