Simulations of Bivariate Archimedean Copulas from Their Nonparametric Generators for Loss Reserving under Flexible Censoring
Bibliographic record
Abstract
With insurers benefiting from ever-larger amounts of data of increasing complexity, we explore a data-driven method to model dependence within multilevel claims in this article. More specifically, we extend the nonparametric estimator for Archimedean copula generators and graphical copula selection procedure introduced by Genest and Rivest to flexible censoring scenarios, using techniques derived from survival analysis. We then propose an alternative method that forgoes any parametric assumption by directly simulating from the estimator of the generator function, using algorithms based on inverse Laplace-Stieltjes transforms. In this article, we focus on a bivariate application and illustrate the performance of our approach with an analysis of a recent Canadian automobile insurance dataset, in which we seek to incorporate the dependence between the activation delays of correlated coverages in a claims reserving framework. We explore the impact on the reserve estimates of performing simulations directly from our nonparametric estimator of the Archimedean copula generator function compared to simulations from a known parametric copula.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.006 | 0.025 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 source (direct Gemma or distilled Codex), 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".