Risk Measures of Stop-loss and Limited Loss Random Variables under Model Uncertainty with Applications in Insurance
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Bibliographic record
Abstract
In this thesis, our focus is on the optimization of reinsurance design, accounting for the \ninfluence of model uncertainty. The following chapters outline our approach: \nIn Chapter 2, we identify the worst-case distributions for both insurers and reinsurers \nby assuming that insurers and reinsurers respectively have their own uncertainty sets. \nThese distributions are structured to maximize their respective shares of the total loss, \nassessed by a distortion risk measure. We consider a reinsurance contract structured as \na stop-loss treaty with a deductible. Our uncertainty sets adopt traditional two-moment \ncharacteristics, incorporated with distance constraints defined using Wasserstein distance. \nWe provide numerical solutions for the worst-case distributions in a general scenario, along \nwith analytical solutions for cases when uncertainty sets only have constraints on the first \ntwo moments of the underlying loss random variable. Based on that, we find the optimal \nstop-loss reinsurance policy from the perspective of the insurer taking model uncertainty \ninto account. \nIn Chapter 3, we assume that uncertainty sets of insurers and reinsurers are defined \nonly by Wasserstein distance. We consider the worst-case risk measures of limited stoploss functions and determine the worst-case distributions for both insurers and reinsurers \nunder limited stop-loss reinsurances. In addition, by conducting numerical experiments, we \nexplore how the limits and deductibles of limited stop-loss reinsurances impact worst-case \nrisk measures for both parties. \nMoving into Chapter 4, we integrate the notion of distribution ambiguity into a negotiation framework, specifically Pareto optimality. Through numerical experiments based on \nresults presented in Chapters 2 and 3, we investigate how the negotiation power between \nparties influences the equilibrium point. \nConcluding our study, the final chapter outlines potential directions for future research \nand development, building upon the foundation laid out in this work.
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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) | 0.000 | 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 it