OPTIMAL REINSURANCE WITH LIMITED CEDED RISK: A STOCHASTIC DOMINANCE APPROACH
Bibliographic record
Abstract
Abstract An optimal reinsurance problem from the perspective of an insurer is studied in this paper, where an upper limit is imposed on a reinsurer's expected loss over a prescribed level. In order to reduce the moral hazard, we assume that both the insurer and the reinsurer are obligated to pay more as the amount of loss increases in a typical reinsurance treaty. We further assume that the optimization criterion preserves the convex order. Such a criterion is very general as most of the criteria for optimal reinsurance problems in the literature preserve the convex order. When the reinsurance premium is calculated as a function of the actuarial value of coverage, we show via a stochastic dominance approach that any admissible reinsurance policy is dominated by a stop-loss reinsurance or a two-layer reinsurance, depending upon the amount of the reinsurance premium. Moreover, we obtain a similar result to Mossin's Theorem and find that it is optimal for the insurer to cede a loss as much as possible under the net premium principle. To further examine the reinsurance premium for the optimal piecewise linear reinsurance policy, we assume the expected value premium principle and derive the optimal reinsurance explicitly under (1) the criterion of minimizing the variance of the insurer's risk exposure, and (2) the criterion of minimizing the risk-adjusted value of the insurer's liability where the liability valuation is carried out using the cost-of-capital approach based on the conditional value at risk.
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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 | 0.004 | 0.007 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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 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".