Dynamic Bayesian Ratemaking: A Markov Chain Approximation Approach
Bibliographic record
Abstract
We contribute to the non-life experience ratemaking literature by introducing a computationally efficient approximation algorithm for the Bayesian premium in models with dynamic random effects, where the risk of a policyholder is governed by an individual process of unobserved heterogeneity. Although intuitive and flexible, the biggest challenge of dynamic random effect models is that the resulting Bayesian premium typically lacks tractability. In this article, we propose to approximate the dynamics of the random effects process by a discrete (hidden) Markov chain and replace the intractable Bayesian premium of the original model by that of the approximate Markov chain model, for which concise, closed-form formula are derived. The methodology is general because it does not rely on any parametric distributional assumptions and, in particular, allows for the inclusion of both the cost and the frequency components in pricing. Numerical examples show that the proposed approximation method is highly accurate. Finally, a real data pricing example is used to illustrate the versatility of the approach.
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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 | 0.023 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
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".