Norm constrained empirical portfolio optimization with stochastic dominance: Robust optimization non-asymptotics
Bibliographic record
Abstract
Abstract This note provides an initial theoretical justification for how <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mi>ℓ</m:mi> </m:mrow> <m:mrow> <m:mi>p</m:mi> </m:mrow> </m:msub> </m:math> {\ell }_{p} -norm regularizations can control the non-asymptotic probability of false dominance (FD) classification in empirically optimal portfolios that satisfy empirical stochastic dominance constraints under an independent and identically distributed setting. The analysis employs a dual characterization of the norm-constrained problem as one of distributionally robust optimization, which enables the application of concentration inequalities involving the Wasserstein distance from the empirical distribution. This approach yields explicit upper bounds for the non-asymptotic FD probability, offering insights into the minimal sample size requirements necessary for maintaining this probability below a pre-specified significance level. The results provide a theoretical framework that outlines directions for future extensions to more general settings involving temporally dependent financial time series.
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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 | 0.013 | 0.066 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 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".