Distortion Risk Measures of Increasing Rearrangement
Bibliographic record
Abstract
Increasing rearrangement is a rewarding instrument in financial risk management. In practice, risks must be managed from different perspectives. A common example is the portfolio risk, which often can be seen from at least two perspectives: market value and book value. Different perspectives with different distributions can be coupled by increasing rearrangement. One distribution is regarded as underlying, and the other distribution can be expressed as an increasing rearrangement of the underlying distribution. Then, the risk measure for the latter can be expressed in terms of the underlying distribution. Our first objective is to introduce increasing rearrangement for application in financial risk management and to apply increasing rearrangement to the class of distortion risk measures. We derive formulae to compute risk measures in terms of the underlying distribution. Afterwards, we apply our results to a series of special distortion risk measures, namely the value at risk, expected shortfall, range value at risk, conditional value at risk, and Wang’s risk measure. Finally, we present the connection of increasing rearrangement with inverse transform sampling, Monte Carlo simulation, and cost-efficient strategies. Butterfly options serve as an illustrative example of the method.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 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".