Fatou Property, representations, and extensions of law-invariant risk\n measures on general Orlicz spaces
Bibliographic record
Abstract
We provide a variety of results for (quasi)convex, law-invariant functionals\ndefined on a general Orlicz space, which extend well-known results in the\nsetting of bounded random variables. First, we show that Delbaen's\nrepresentation of convex functionals with the Fatou property, which fails in a\ngeneral Orlicz space, can be always achieved under the assumption of\nlaw-invariance. Second, we identify the range of Orlicz spaces where the\ncharacterization of the Fatou property in terms of norm lower semicontinuity by\nJouini, Schachermayer and Touzi continues to hold. Third, we extend Kusuoka's\nrepresentation to a general Orlicz space. Finally, we prove a version of the\nextension result by Filipovi\\'{c} and Svindland by replacing norm lower\nsemicontinuity with the (generally non-equivalent) Fatou property. Our results\nhave natural applications to the theory of risk measures.\n
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".