On a Classical Risk Model with a Constant Dividend Barrier
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Bibliographic record
Abstract
Abstract This paper considers a risk model with a constant dividend barrier. It first points out interesting connections between some previous results for this model and those for spectrally negative Lévy processes. An expression is then obtained for the joint distribution of the surplus immediately prior to ruin and the deficit at ruin, discounted from the time of ruin. Such an expression involves known results on the joint distribution at ruin for a classical risk model without barrier. Also discussed are the joint distributions related to the time periods when dividends are paid. In particular, this paper obtains the Laplace transform for the total dividend payments until ruin, and another expression for the expected present value of the total amount of dividend payments until ruin. The results do not require the positive loading condition.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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