Optimal reinsurance design under convex premium principles and distortion risk measures
Bibliographic record
Abstract
This paper studies an optimal reinsurance problem from an insurer’s perspective under convex premium principles. The insurer’s preference is assumed to be dictated by the distortion risk measure. When doing business with only one reinsurer, the general form of the optimal indemnity function for the insurer is derived by jointly applying the calculation of variation and marginal indemnification function approaches. We demonstrate that the optimal indemnity function for the insurer takes the form of a limited stop-loss when the insurer adopts a Range Value-at-Risk preference. In contrast, when the insurer applies strictly convex distortion risk measures, we show that, under mild conditions, the optimal indemnity function may include a co-insurance component. We also extend the results to the case of multiple reinsurers through a representative reinsurer lens, and present a sufficient condition under which the representative reinsurer’s premium principle is of the same mathematical form of the convex premium principle studied in this paper. We also show the connection between the optimal reinsurance problems under the certainty-equivalent premium principle and under the convex premium principle. Some interesting results are presented for the problem between one insurer and multiple reinsurers when each reinsurer applies an i th-moment premium principle.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".