带跳的全耦合McKean-Vlasov正倒向随机微分方程在全解元组律依赖下的适定性
Well-posedness of fully coupled McKean-Vlasov FBSDEs with jumps under full-tuple law dependence
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中文总结 AI 辅助
该研究证明了带跳全耦合McKean-Vlasov正倒向随机微分方程在全解元组律依赖下的适定性，通过单调延拓方法建立相关估计与存在唯一性，并给出均值场经销商市场示例验证其非微扰律依赖特性。
中文摘要 AI 辅助
我们证明了带跳的全耦合McKean-Vlasov正倒向随机微分方程的存在性、唯一性与稳定性，该方程的漂移项、扩散项、跳项及驱动项系数可在二次Wasserstein距离下关于全解元组Θ=(X,Y,Z,U)的联合律满足Lipschitz连续，其中X为前向状态，Y为倒向变量，Z为布朗积分项，U为L²(ν)值跳积分项；终端函数可关于X_T及其律满足Lipschitz连续。该系统由布朗运动与独立的补偿泊松随机测度驱动，后者具有任意σ有限强度，允许无穷跳活动。Lipschitz与单调性假设仅施加于对角元组律对(Θ,Law(Θ))，我们证明期望对角单调性严格弱于逐点单调性。在带跳扩展的G单调性条件下，通过从弱耦合基例出发对耦合强度进行单调延拓，我们建立了先验连续依赖估计、唯一性及任意给定有限时间域上的存在性。一个均值场经销商市场示例非微扰地实现了U-律依赖：其律交互在任意交互强度下均为单调，且其标记测度具有无穷活动。
英文摘要
We prove existence, uniqueness, and stability for fully coupled McKean-Vlasov forward-backward SDEs with jumps whose drift, diffusion, jump, and driver coefficients may depend Lipschitz-continuously, in quadratic Wasserstein distance, on the joint law of the full solution tuple $Θ=(X,Y,Z,U)$: forward state, backward variable, Brownian integrand, and $L^2(ν)$-valued jump integrand. The terminal function may depend Lipschitz-continuously on $X_T$ and its law. The system is driven by a Brownian motion and an independent compensated Poisson random measure with arbitrary $σ$-finite intensity, so infinite jump activity is admitted. Both the Lipschitz and monotonicity hypotheses are imposed only along diagonal tuple-law pairs $(Θ,\mathrm{Law}(Θ))$; we show that expected diagonal monotonicity is strictly weaker than pointwise monotonicity. Under a jump-extended $G$-monotonicity condition we establish an a priori continuous-dependence estimate, uniqueness, and existence on every prescribed finite horizon, by monotone continuation in the coupling strength from a small-coupling base case. A mean-field dealer-market example realises the $U$-law dependence non-perturbatively: its law interaction is monotone at every interaction strength, and its mark measure has infinite activity.
