Structural properties of multi-period martingale optimal transport problems and applications
Bibliographic record
Abstract
This paper develops new tools to study the structural properties of solutions to multi-period martingale optimal transport (MOT) problems. More precisely, conditions are obtained on how and when two-period martingale couplings may be glued together to obtain multi-period martingales and which among these gluings are optimal for particular MOT problems. Together with a novel linearization of the optimal cost as certain terms vanish, these gluing are used to obtain a complete characterization of limiting solutions in a three-period problem as the interaction between two of the variables vanishes. For the full three-period problem, several structural and uniqueness results under a variety of different assumptions on the marginals and cost function are also obtained. For high-dimensional input data, these approximation methods, if compared with classic direct numerical approximations, are cost-efficient. To illustrate the practicality of these results approximate model independent upper and lower bounds are computed for options prices depending on Amazon stock prices at three different times.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| 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".