Multivariate Bühlmann-Straub credibility model for claim reserving
Bibliographic record
Abstract
Abstract One of the approaches that is used for claim reserving in insurance companies is credibility theory, which allows claim reserving by combining claim payment data with other information. In this paper, the Bühlmann-Straub credibility model is used. Furthermore, in general, claim reserving in a company is done by calculating the claim reserve in each line of business (LoB) in the company, then the total claim reserve for the company (aggregate reserve) is obtained by adding up the claim reserve in each LoB. Considering the possibility that there is correlation between the existing LoBs, the value of aggregate reserve can actually be less than the sum of the claim reserve in each of the existing LoB. Therefore, research on the claim reserving then evolves by considering claim payment data from various LoBs in a company, or also called claim reserving in multivariate context. In this paper, a research is conducted on the development of multivariate Bühlmann-Straub credibility model for claim reserving along with estimation for model’s parameters. The model is used to calculate claim reserve for three LoBs of insurance company in United State, based on the data of claim amount during the period of 2008-2017 that was published by Association of Insurance Commisioners of the United State. It appears that the error of multivariate Bühlmann-Straub credibility model is lower than the error of standard Bühlmann-Straub credibility model.
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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 | 0.008 | 0.030 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".