An efficient approach to quantile capital allocation and sensitivity analysis
Why this work is in the frame
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Bibliographic record
Abstract
Abstract In various fields of applications such as capital allocation, sensitivity analysis, and systemic risk evaluation, one often needs to compute or estimate the expectation of a random variable, given that another random variable is equal to its quantile at some prespecified probability level. A primary example of such an application is the Euler capital allocation formula for the quantile (often called the value‐at‐risk), which is of crucial importance in financial risk management. It is well known that classic nonparametric estimation for the above quantile allocation problem has a slower rate of convergence than the standard rate. In this paper, we propose an alternative approach to the quantile allocation problem via adjusting the probability level in connection with an expected shortfall. The asymptotic distribution of the proposed nonparametric estimator of the new capital allocation is derived for dependent data under the setup of a mixing sequence. In order to assess the performance of the proposed nonparametric estimator, AR‐GARCH models are proposed to fit each risk variable, and further, a bootstrap method based on residuals is employed to quantify the estimation uncertainty. A simulation study is conducted to examine the finite sample performance of the proposed inference. Finally, the proposed methodology of quantile capital allocation is illustrated for a financial data set.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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 | 0.001 |
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 it