Claims Reserving When There Are Negative Values in the Runoff Triangle
Why this work is in the frame
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Bibliographic record
Abstract
Abstract This paper is concerned with the situation that occurs in claims reserving when there are negative values in the development triangle of incremental claim amounts. Typically these negative values will be the result of salvage recoveries, payments from third parties, total or partial cancellation of outstanding claims due to initial overestimation of the loss or to a possible favorable jury decision in favor of the insurer, rejection by the insurer, or just plain errors. Some of the traditional methods of claims reserving, such as the chain-ladder technique, may produce estimates of the reserves even when there are negative values. However, many methods can break down in the presence of enough (in number and/or size) negative incremental claims if certain constraints are not met. Historically the chain-ladder method has been used as a gold standard (benchmark) because of its generalized use and ease of application. A method that improves on the gold standard is one that can handle situations where there are many negative incremental claims and/or some of these are large. This paper presents a Bayesian model to consider negative incremental values, based on a three-parameter log-normal distribution. The model presented here allows the actuary to provide point estimates and measures of dispersion, as well as the complete distribution for outstanding claims from which the reserves can be derived. It is concluded that the method has a clear advantage over other existing methods. A Markov chain Monte Carlo simulation is applied using the package WinBUGS.
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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 | 0.005 | 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 | 0.002 | 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