VAR and CTE Criteria for Optimal Quota-Share and Stop-Loss Reinsurance
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Bibliographic record
Abstract
Abstract It is well known that reinsurance can be an effective risk management tool for an insurer to minimize its exposure to risk. In this paper we provide further analysis on two optimal reinsurance models recently proposed by Cai and Tan. These models have several appealing features including (1) practicality in that the models could be of interest to insurers and reinsurers, (2) simplicity in that optimal solutions can be derived in many cases, and (3) integration between banks and insurance companies in that the models exploit explicitly some of the popular risk measures such as value-at-risk and conditional tail expectation. The objective of the paper is to study and analyze the optimal reinsurance designs associated with two of the most common reinsurance contracts: the quota share and the stop loss. Furthermore, as many as 17 reinsurance premium principles are investigated. This paper also highlights the critical role of the reinsurance premium principles in the sense that, depending on the chosen principles, optimal quota-share and stop-loss reinsurance may or may not exist. For some cases we formally establish the sufficient and necessary (or just sufficient) conditions for the existence of the nontrivial optimal reinsurance. Numerical examples are presented to illustrate our results.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 it