Technical Note—An Unexpected Stochastic Dominance: Pareto Distributions, Dependence, and Diversification
Bibliographic record
Abstract
Diversification is generally regarded as an efficient tool to reduce portfolio risks. In “An unexpected stochastic dominance: Pareto distributions, dependence, and diversification,” Chen, Embrechts, and Wang showed that the weighted average of independent and identically distributed (i.i.d.) Pareto random variables with infinite mean is larger than one such random variable in the sense of first-order stochastic dominance, and thus diversification is, surprisingly, worse than no diversification. The relation implies superadditivity of value-at-risk, a regulatory risk measure used in the finance and insurance sectors. The obtained relation also holds under some form of negative dependence.
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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 | 0.004 | 0.016 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.001 | 0.004 |
| 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".