Pareto efficiency and financial fairness under limited expected loss constraint
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Bibliographic record
Abstract
This paper investigates the Pareto efficiency and financial fairness in a collective asset allocation under a limited expected loss (LEL) constraint. By studying a constrained collective optimization problem, we characterize a constrained version of Pareto optimality, named LEL-Pareto optimality, within the admissible class of sharing rules. We propose a novel sharing rule, referred to as the LEL sharing rule, as an alternative to widely used proportional sharing rules. We rigorously demonstrate that every LEL sharing rule is LEL-Pareto-optimal and vice versa, thereby establishing a novel Borch-like criterion in a risk-constrained setting. Under the financial fairness condition, we derive a unique LEL sharing rule through a fixed-point iteration scheme by solving a highly non-linear system of Lagrange multipliers related to LEL-constrained optimization for collective utility and the financial fairness condition. Under mild conditions, we achieve global convergence and establish the existence of a unique fixed point of the iterative algorithm. Our numerical analysis affirms the theoretical findings and underscores the positive influence of the LEL constraint among prevalent proportional sharing rules, emphasizing the importance of risk control in practical scenarios.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 it