Abstract The goal of this paper is to study a stochastic game connected to a system of forward-backward stochastic differential equations (FBSDEs) involving delay and noisy memory. We derive sufficient and necessary maximum principles for a set of controls for the players to be a Nash equilibrium in the game. Furthermore, we study a corresponding FBSDE involving Malliavin derivatives. This kind of equation has not been studied before. The maximum principles give conditions for determining the Nash equilibrium of the game. We use this to derive a closed form Nash equilibrium for an economic model where the players maximize their consumption with respect to recursive utility.

中文翻译：

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具有延迟和噪声记忆的前向后向随机微分方程游戏

摘要 本文的目标是研究一个随机博弈，该博弈与一个涉及延迟和噪声记忆的前向-后向随机微分方程 (FBSDE) 系统相连。我们为博弈中的纳什均衡对一组控制推导出了充分且必要的最大原则。此外，我们研究了涉及 Malliavin 衍生物的相应 FBSDE。这种方程以前没有研究过。最大值原则给出了确定博弈的纳什均衡的条件。我们使用它来推导出一个经济模型的封闭形式纳什均衡，其中参与者在递归效用方面最大化他们的消费。