The optimal reinsurance strategy with price-competition between two reinsurers
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Bibliographic record
Abstract
We study optimal reinsurance for an insurer and two reinsurers in the market through stochastic game theory. The relationship between the insurer and reinsurers is described by a Stackelberg model, where reinsurers, as market leaders, set prices for reinsurance treaties, and the insurer, as a price taker, determines reinsurance demand. Furthermore, we employ a Nash game to model the price competition between the two reinsurers who adopt different premium principles: the variance premium principle and the expected value premium principle. Both the insurer and reinsurers aim to maximize their respective mean-variance cost functions, leading to a time inconsistency control problem. This issue is resolved using a corresponding extended Hamilton-Jacobi-Bellman equation in the game-theoretic framework. We find that the insurer will adopt propositional and excess-of-loss reinsurance strategies with two reinsurers, respectively. Moreover, under an exponential claim size distribution, there exists a unique equilibrium reinsurance premium strategy. Our numerical analysis illuminates the effects of claim size, risk aversion, and the interest rates of the insurer and reinsurers on the equilibrium reinsurance and premium strategies, enhancing the understanding of competition in the reinsurance market.
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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 | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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