Approximation of the Ultim Ruin Probability by the Finite Difference Method of a Variable-memory Process (HAWKES process) With a Distribution of WEIBULL
Bibliographic record
Abstract
In insurance risk management, the probability of ruin is a very important metric to assess. In this article, we give an approximation of the probability of ruin at the infinite horizon, where the inter-arrivals of claims follow the HAWKES process and the amount of claims follows the WEIBULL distribution, with independence between its two processes. This approximation is made using numerical analysis methods, it consists in solving a second-order integro-differential equation of which two cases are considered on the parameterηof WEIBULL: ifηis equal to 1, then the distribution of the amounts of claims is exponential, which brings us back to the risk model established in Badini et al. (2024). On the other hand, ifηis greater than 1, then the results lead us to a system of linear equations for which we use the finite di_erence method to obtain a numerical solution. This method is used in both cases (η = 1 andη> 1) for u ranging from 0 to 100, so we obtain the analytical solution.
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How this classification was reachedexpand
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 | 0.005 | 0.009 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".