Bowley solution of a variance game in insurance
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Bibliographic record
Abstract
In this paper, we study a Stackelberg game for insurance contracting. Specifically, we assume that the insurance buyer and seller hold generalized mean-variance preferences and the premium is determined by a generalized variance premium principle. Under mild conditions, we derive the Bowley solution, which consists of the optimal indemnity and pricing functions, for the Stackelberg game. We also compare the Bowley solution with the Pareto optimal solution and prove that the Bowley solution can never be Pareto optimal. This finding shows the inefficiency of Stackelberg games in insurance contracting, which echoes the existing results derived in other settings. We present two specific examples to further show the implications of our main results as well as the sensitivity of the Bowley and Pareto optimal solutions with respect to the model parameters.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| 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