Pareto-optimal insurance with an upper limit on the insurer's exposure
Why this work is in the frame
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Bibliographic record
Abstract
We examine the problem of determining Pareto-optimal (PO) insurance contracts when the insurer imposes an ex ante upper limit on disbursement. The problem is similar in spirit to that of Cummins & Mahul (2004), but it extends it in two directions: first, we use the more general and more flexible class of distortion premium principles; and second, we allow for heterogeneity in beliefs between the insurer and the insured. We unify the settings of Ghossoub (2019a, 2019b), and we adapt the approaches therein to encompass the case of a policy limit. First, we show that PO contracts are those that result from a budget-constrained optimization problem for the DM. We then provide a closed-form characterization of optimal contracts. Our result is similar in spirit to that of Cummins & Mahul (2004), who show that when policy limits are introduced to Arrow's model, PO contracts are limited deductible contracts. While Ghossoub (2019a, 2019b) shows that variable deductible contracts are optimal, the results of the present paper indicate that limited variable deductible contracts are optimal when policy limits are present. We illustrate our results via numerical examples.
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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 | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
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