Applications of Population Sampling to Ratemaking and Reserving in General Insurance
Bibliographic record
Abstract
Insurance ratemaking and reserving are critical to the financial stability of insurers, ensuring that premiums accurately reflect policyholder risk while maintaining sufficient reserves for future claims. Traditionally, these processes have relied on simplistic basic methods—such as experience rating tables and development factor techniques—that struggle to address the complexities of modern insurance markets. The increasing availability of granular, high-dimensional data demands more advanced statistical methodologies that enhance predictive accuracy while overcoming significant computational challenges. This thesis makes three major contributions by introducing population sampling—a powerful yet underutilized statistical methodology in actuarial science—to address key methodological, computational, and predictive challenges in ratemaking and reserving. The first contribution develops a scalable Bayesian experience rating framework for large, heterogeneous non-life insurance portfolios. It introduces a likelihood-based summary statistic that integrates policyholder heterogeneity—arising from individual attributes and claim history—into a single quantity. This statistic is shown to possess properties similar to sufficient statistics. By combining population sampling with surrogate modelling and this summary statistic, the approach drastically reduces the computational burden of Bayesian premium estimation while preserving accuracy. The methodology is validated with an European auto insurance data. The second contribution reconceptualizes claim reserving (RBNS and IBNR) as a population sampling problem, offering a paradigm shift in reserve estimation and integrating it with broader statistical foundations. This leads to the development of an inverse probability weighting estimator, which corrects for policyholder heterogeneity within the Chain-Ladder framework, modernizing this classic technique. The third contribution extends this perspective, introducing a framework for claim reserving built on population sampling. It proposes an augmented inverse probability weighting estimator, unifying aggregate and individual models, and bridging the gap between these two reserving approaches. This enables highly granular reserve estimation while addressing sampling bias from incomplete claims data, improving predictive accuracy and actuarial robustness. Effectiveness is demonstrated using real data from European and Canadian markets. By leveraging population sampling, this thesis establishes new statistical tools for ratemaking and reserving, bridging actuarial practice with modern data-driven approaches. These advancements enhance computational efficiency and predictive precision, providing a rigorous foundation for the future of actuarial modelling.
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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 | 0.003 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".