Optimal dynamic risk sharing under the time‐consistent mean‐variance criterion
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Bibliographic record
Abstract
Abstract In this paper, we consider a dynamic Pareto optimal risk‐sharing problem under the time‐consistent mean‐variance criterion. A group of n insurers is assumed to share an exogenous risk whose dynamics is modeled by a Lévy process. By solving the extended Hamilton–Jacobi–Bellman equation using the Lagrange multiplier method, an explicit form of the time‐consistent equilibrium risk‐bearing strategy for each insurer is obtained. We show that equilibrium risk‐bearing strategies are mixtures of two common risk‐sharing arrangements, namely, the proportional and stop‐loss strategies. Their explicit forms allow us to thoroughly examine the analytic properties of the equilibrium risk‐bearing strategies. We later consider two extensions to the original model by introducing a set of financial investment opportunities and allowing for insurers' ambiguity towards the exogenous risk distribution. We again explicitly solve for the equilibrium risk‐bearing strategies and further examine the impact of the extension component (investment or ambiguity) on these strategies. Finally, we consider an application of our results in the classical risk‐sharing problem of a pure exchange economy.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.002 |
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