Model Aggregation for Risk Evaluation and Robust Optimization
Bibliographic record
Abstract
We introduce a new approach for prudent risk evaluation based on stochastic dominance, and it is called the model aggregation (MA) approach. In contrast to the classic worst case risk (WR) approach, the MA approach produces not only a robust value of risk evaluation but also a robust distributional model, independent of any specific risk measure. The MA risk evaluation can be computed through explicit formulas in the lattice theory of stochastic dominance, and under some standard assumptions, the MA robust optimization admits a convex program reformulation. The MA approach for Wasserstein and mean-variance uncertainty sets admits explicit formulas for the obtained robust models. Via an equivalence property between the MA and WR approaches, new axiomatic characterizations are obtained for the value at risk and the expected shortfall (also known as conditional value at risk). The new approach is illustrated with various risk measures and examples from portfolio optimization. This paper was accepted by Chung Piaw Teo, optimization. Funding: This research was supported by the National Natural Science Foundation of China [Grants 12371476, 71921001, 71671176, 71871208], the Natural Sciences and Engineering Research Council of Canada [Grants CRC-2022-00141, RGPIN-2024-03728, RGPAS-2018-522590, RGPIN-2018-03823], and the Society of Actuaries Center of Actuarial Excellence Research Grant. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.03523 .
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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 | 0.007 | 0.013 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.005 | 0.006 |
| Open science | 0.002 | 0.005 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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".