Weighted intermediate rank lattice rules with applications in finance
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Bibliographic record
Abstract
This paper considers the intermediate-rank lattice rules or higher rank lattice rules under the weighted Korobov space by extending the weighted higher rank lattice rule (WHRLR) to the general case with composite integer n so that the number of quadrature points is N = Lr n, where r is the rank of the rule and l is a positive integer such that gcd(n, l) = 1. We obtain a general expression for the average of Mn, d, copy(l, r) over a subset of Zd, and give an upper bound and strong tractability for WHRLR. These results extend the work of Kuo & Joe ([1] and [2]). By applying to option pricing, our numerical results indicate that WHRLR has some advantages over the weighted rank-1 good lattice rule and is competitively more efficient than the standard Monte Carlo method and the Sobol' sequence based quasi-Monte Carlo method.
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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 | 0.000 | 0.000 |
| 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