We study optimal control for mean-field forward backward stochastic differential equations with payoff functionals of mean-field type. Sufficient and necessary optimality conditions in terms of a stochastic maximum principle are derived. As an illustration, we solve an optimal portfolio with mean-field risk minimization problem.

中文翻译：

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平均场 FBSDE 和最优控制

我们研究了具有平均场类型支付函数的平均场前向后向随机微分方程的最优控制。根据随机最大值原理推导出充分和必要的最优条件。作为说明，我们解决了具有平均场风险最小化问题的最优投资组合。