Application of the convolution operator for scenario integration with loss data in operational risk modeling
Why this work is in the frame
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Bibliographic record
Abstract
When using the advanced measurement approach to determine required regulatory capital for operational risk, expert opinion is applied via scenario analysis to help quantify exposure to high-severity events. A methodology is presented that makes use of the convolution operator to integrate scenarios into a baseline model. Using a baseline loss distribution model calibrated on historical losses and a scenario-derived loss distribution calibrated on scenario data points, the addition of both random processes equates to the convolution of the corresponding densities. Using an analogy from digital signal processing, the commutative property of convolution allows one function to smooth and average the other. The inherent uncertainty in scenario analysis has caused concern amongst practitioners when too much emphasis has been placed on absolutes in terms of quantified frequency/severity estimates. This method addresses this uncertainty and produces a combined loss distribution that takes information from the entire domain of the calibrated scenario distribution. The necessary theory is provided within and an example is shown to provide context.
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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 | 0.004 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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