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 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 | 0.017 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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".