On the surplus prior to ruin in the perturbed classical risk process
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Purpose The purpose of this article is to consider the classical risk model that is perturbed by a Brownian motion process. The article derives explicit formulas for the joint and marginal probability density functions of the surplus prior to ruin and the deficit at ruin. Design/methodology/approach This article first extends the dual argument to probabilistically explain the symmetry between the two random variables related to the so‐called modified ladder height. Then the paper uses renewal arguments to derive the joint distribution of the surplus prior to ruin and the deficit at ruin. Findings The study derived an explicit formula for the undiscounted joint density in the perturbed risk model that is directly parallel to formula (3.2) for the classical risk model. The formula clearly shows that in a perturbed risk process, when ruin is caused by a claim, the p.d.f. of the surplus prior to ruin is continuous. In addition, shows that when the claim sizes follow a phase‐type distribution, all the relevant quantities can be conveniently computed. Originality/value The dual argument used in this article is novel. The formula first clearly shows that in the perturbed risk model, the p.d.f. of the surplus prior to ruin is continuous. When claim sizes are phase‐type, the formulas can be conveniently computed.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.040 | 0.016 |
| 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 | 0.003 | 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