AI 中文总结
该研究针对带可选障碍和$L^p$数据的平均场双反射正倒向随机微分方程，在短时间区间和全局时间下分别证明了解的存在唯一性，其结果可应用于递归平均场Dynkin博弈与博弈期权估值。
AI 中文摘要
我们研究满足强Mokobodzki条件的带两个可选障碍的平均场双反射正倒向随机微分方程。对于$p\in(1,2]$的$L^p$数据，当系数依赖于$(X,Y,Z)$的联合分布时，我们在足够短的时间区间上证明了其存在唯一性。在额外的单调性条件下，利用指数加权范数，我们还得到了$p=2$时的全局时间结果。该设定受递归平均场Dynkin博弈和带有不规则收益障碍的博弈期权估值的启发。
英文摘要
We study mean-field doubly reflected forward-backward stochastic differential equations with two optional barriers satisfying a strong Mokobodzki condition. For $L^p$-data, $p\in(1,2]$, we prove existence and uniqueness on sufficiently short time horizons when the coefficients may depend on the joint law of $(X,Y,Z)$. Under an additional monotonicity condition and using an exponentially weighted norm, we also obtain a global-in-time result for $p=2$. The setting is motivated by recursive mean-field Dynkin games and game-option valuation with irregular payoff barriers.
