Efficient computations of multivariate normal distributions with applications to finance
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Bibliographic record
Abstract
This paper discusses the simulation of multivariate normal distributions with applications to Finance. We found that all the bivariate normal distributions can be converted into the one dimensional integrals and most cases of the trivariate normal distributions can be converted into 1- dimensional integrals provided |λi| < 1 (i = 1, 2, 3), where ρij: = λiλj(i ≠ j) are correlation coefficients. If the dimension is higher than 3, the Monte Carlo and Quasi-Monte Carlo methods can be applied to estimate these distributions. And the quasi-Monte Carlo methods are more efficient than the Monte Carlo method. We also discuss the applications in finance since in many situations, financial derivatives, such as options, can be expressed in terms of multivariate normal distributions. Similar ideas can be applied to the computations of multivariate t-distributions.
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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