A Flexible Hierarchical Insurance Claims Model with Gradient Boosting and Copulas
Bibliographic record
Abstract
Predicting future claims is an important task for actuaries, and sophisticating the claim modeling process allows insurers to be more competitive and to stay financially sound.We propose a hierarchical claim model that refines traditional methods by considering dependence between payment occurrences with a multinomial distribution and between payment amounts with copulas.We perform prediction with covariates using XGBoost, a scalable gradient boosting algorithm, gaining predictive power over the frequently used generalized linear models.The model construction and fitting is illustrated with a real auto insurance dataset from a large Canadian insurance company.The use of XGBoost is well suited for such big data containing a lot of insureds and covariates.To our knowledge, the validity of the copula inference with gradient boosting margins has not been demonstrated in past literature, so we perform simulation studies to assess the performance of methods based on ranks of residuals.We show some applications of our model and compare the performance with reference models.Results show that the dependence components of our model improve the segmentation quality and better replicate the global stochasticity.
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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 | 0.000 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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".