Optimal Reinsurance Design under Ambiguity and Value-at-Risk Preference with Wasserstein and <i> L <sup>k</sup> </i> Distance Metrics
Bibliographic record
Abstract
This article delves into the optimal reinsurance problem from the perspective of a decision maker (DM) who exhibits a preference for value-at-risk (VaR) and experiences ambiguity regarding the underlying loss distribution. The uncertainty set considered in this study encompasses distributions that closely envelop a reference distribution, with the proximity quantified using the Wasserstein metric. Through a rigorous analysis, we present a thorough characterization of both the optimal indemnity function and the worst-case VaR for our proposed problem. Furthermore, we extend our examination to a pertinent problem wherein the Lk distance metric substitutes for the Wasserstein metric. Numerical examples are provided to demonstrate the implications of our main findings, and a comparative analysis is conducted with relevant literature to further enhance our understanding of the outcomes. Explicit comparative analysis demonstrates that Wasserstein ambiguity sets minimize worst-case VaR through aggregate tail mass shifting penalties, while Lk distance ambiguity sets prioritize local distributional shifts near the VaR quantile, generating higher worst-case VaR estimates particularly sensitive to extreme-loss scenarios. The insights and analytical tools elucidated in this article hold consequential implications for insurers and reinsurers in proficiently navigating risk management within an uncertain environment.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".