Analysis of IBNR claims in renewal insurance models
Bibliographic record
Abstract
Incurred but not reported (IBNR) claims, which arise naturally in insurance contexts, are of central importance to insurers for risk management and financial reporting purposes. In this paper, we first examine the moments of the total discounted IBNR claim amount at a given time when claim events occur according to a compound renewal process. Under the same claim arrival dynamic, we later consider the joint moments of the total discounted IBNR claim amount and the total incurred and reported claim amount at possibly different time points, a quantity of much interest for claim reserving purposes. In the second part of this article, we examine in more detail properties of the IBNR claim number under specific distributional assumptions for the reporting lags and the interarrival times. Among others, the self-decomposability of the IBNR claim number process is considered when claim events occur according to a compound Poisson process.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".