跳损、重建价格不确定性与群体交互下的动态实物对冲
Dynamic Physical Hedging amid Jump Losses, Reconstruction-Price Uncertainty, Population Interactions
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中文总结 AI 辅助
本文针对同时面临巨灾损失与随机重建成本的保险公司，通过平均场博弈（MFG）方法建立耦合HJB-柯尔莫哥洛夫系统，研究动态实物对冲，数值实验揭示了重建成本等因素对最优对冲及均衡成本的影响。
中文摘要 AI 辅助
我们研究同时面临巨灾损失与随机重建成本的保险公司的动态实物对冲问题。盈余演化是受控跳跃扩散过程，其损失幅度结合了标记的巨灾严重度、外生均值回复成本因子与内生风险缓释。我们建立适定性、矩与稳定性估计，以及停时动态规划原理，并证明值函数是所得非局部哈密尔顿-雅可比-贝尔曼（HJB）方程的唯一粘性解。通过具有简化形式脆弱性成本的平均场博弈（MFG）引入策略交互，得到耦合的后前向HJB-柯尔莫哥洛夫系统。我们在适当紧性与单调性条件下建立松弛均衡存在性、马尔可夫实现与唯一性。数值实验显示，重建成本与资本充足度显著影响最优对冲，而截面脆弱性改变均衡成本；尾族鲁棒性计算进一步评估这些结论对不同巨灾严重度设定的敏感性。
英文摘要
We study dynamic physical hedging for insurers exposed jointly to catastrophe losses and stochastic reconstruction costs. Surplus evolves as a controlled jump diffusion whose loss amplitude combines marked catastrophe severity, an exogenous mean-reverting cost factor, and endogenous mitigation. We establish well-posedness, moment and stability estimates, and a stopping-time dynamic programming principle, and prove that the value function is the unique viscosity solution of the resulting nonlocal Hamilton-Jacobi-Bellman (HJB) equation Strategic interaction is introduced through a mean field game (MFG) with reduced-form vulnerability costs, yielding a coupled backward-forward HJB-Kolmogorov system. We establish relaxed equilibrium existence, Markovian realization, and uniqueness under appropriate compactness and monotonicity conditions. Numerical experiments show that reconstruction costs and capitalization materially affect optimal hedging and that cross-sectional vulnerability alters equilibrium costs. Tail-family robustness calculations further assess the sensitivity of these conclusions to alternative catastrophe-severity specifications.
