Reinsurance games with two reinsurers: Tree versus chain
Bibliographic record
Abstract
This paper studies reinsurance contracting and competition in a continuous-time model with ambiguity. The market consists of one insurer and two reinsurers, who apply a generalized expected-value premium principle and a generalized variance premium principle to price reinsurance contracts, respectively. The reinsurance contracting problems between the insurer and reinsurers are resolved by Stackelberg differential games, and the reinsurance competition between two reinsurers is settled by a non-cooperative Nash game. We obtain the closed-form equilibrium strategies for all three players under both a tree structure and a chain structure. A detailed comparison study reveals that the tree structure is preferred to the chain structure from a social planner’s perspective, and the tree structure is generally preferred from the insurer’s perspective.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.004 | 0.003 |
| Insufficient payload (model declined to judge) | 0.007 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".