Asymptotic Correlation Structure of Discounted Incurred But Not Reported Claims under Fractional Poisson Arrival Process
Bibliographic record
Abstract
This paper studies the joint moments of a compound discounted renewal process\nobserved at different times with each arrival removed from the system after a\nrandom delay. This process can be used to describe the aggregate (discounted)\nIncurred But Not Reported claims in insurance and also the total number of\ncustomers in an infinite server queue. It is shown that the joint moments can\nbe obtained recursively in terms of the renewal density, from which the\ncovariance and correlation structures are derived. In particular, the\nfractional Poisson process defined via the renewal approach is also considered.\nFurthermore, the asymptotic behaviour of covariance and correlation coefficient\nof the aforementioned quantities is analyzed as the time horizon goes to\ninfinity. Special attention is paid to the cases of exponential and Pareto\ndelays.\n
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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 | 0.001 | 0.001 |
| 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 | 0.001 |
| 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".