具有风险相互依存性的保险委托-代理平均场博弈模型
A Principal-Agent Mean-Field Game Model of Insurance with Risk Interdependence
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中文总结 AI 辅助
研究道德风险、内生参与和战略风险相互依存下的保险合同设计问题，用异质平均场博弈近似战略互动，建立下层均衡存在性与唯一性，嵌入上层优化问题，证明相关均衡存在，扩展到有限合同菜单，表明多合同筛选可提高委托人预期收益。
中文摘要 AI 辅助
我们研究了道德风险、内生参与和战略风险相互依存下的保险合同设计问题。由于由此产生的N人博弈存在维度诅咒，我们通过异质平均场博弈来近似战略互动。利用可测选择论证和卡库塔尼不动点定理，严格建立了下层平均场纳什均衡的存在性。通过证明总参与阈值的L^1-利普希茨连续性，进一步通过压缩映射建立了均衡唯一性。然后将这种平均场响应嵌入到保险人的上层斯塔克尔伯格优化问题中。通过一般性能包络来制定目标，以适应潜在的均衡多重性，证明上层ε-最优合同的存在性，并在唯一性条件下证明精确斯塔克尔伯格均衡的存在性。最后将模型扩展到有限合同菜单，提供了数值证据表明多合同筛选提高了相互依存风险环境中委托人的预期收益。
英文摘要
We study an insurance contract-design problem under moral hazard, endogenous participation, and strategic risk interdependence. Because the resulting $N$-agent game suffers from the curse of dimensionality, we approximate the strategic interactions via a heterogeneous mean-field game. We rigorously establish the existence of a lower-level mean-field Nash equilibrium using measurable selection arguments and the Kakutani fixed-point theorem. By proving the $L^1$-Lipschitz continuity of the aggregate participation threshold, we further establish equilibrium uniqueness via a contraction mapping. We then embed this mean-field response into the insurer's upper-level Stackelberg optimization problem. We formulate the objective through general performance envelopes to accommodate potential equilibrium multiplicity, proving the existence of upper-level $\varepsilon$-optimal contracts, and demonstrating the existence of an exact Stackelberg equilibrium under the uniqueness regime. We conclude by extending the model to finite contract menus, providing numerical evidence that multi-contract screening improves the principal's expected payoff in interdependent risk environments.
