We study a general class of fully coupled backward–forward stochastic differential equations of mean-field type (MF-BFSDE). We derive existence and uniqueness results for such a system under weak monotonicity assumptions and without the non-degeneracy condition on the forward equation. This is achieved by suggesting an implicit approximation scheme that is shown to converge to the solution of the system of MF-BFSDE. We apply these results to derive an explicit form of open-loop Nash equilibrium strategies for nonzero sum mean-field linear-quadratic stochastic differential games with random coefficients. These strategies are valid for any time horizon of the game.

中文翻译：

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平均场后向-前向随机微分方程和非零和随机微分博弈

我们研究了一类一般的平均场型完全耦合的后向-前向随机微分方程（MF-BFSDE）。我们在弱单调性假设和前向方程没有非退化条件的情况下推导出这样一个系统的存在性和唯一性结果。这是通过提出一个隐式逼近方案来实现的，该方案显示收敛到 MF-BFSDE 系统的解。我们应用这些结果推导出具有随机系数的非零和平均场线性二次随机微分博弈的开环纳什均衡策略的显式形式。这些策略适用于游戏的任何时间范围。