<p style='text-indent:20px;'>In this study, we have analyzed a market impact game between <i>n</i> risk-averse agents who compete for liquidity in a market impact model with a permanent price impact and additional slippage. Most market parameters, including volatility and drift, are allowed to vary stochastically. Our first main result characterizes the Nash equilibrium in terms of a fully coupled system of forward-backward stochastic differential equations (FBSDEs). Our second main result provides conditions under which this system of FBSDEs has a unique solution, resulting in a unique Nash equilibrium.</p>

中文翻译：

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具有随机参数的市场影响博弈的 FBSDE 方法

<p style='text-indent:20px;'>在这项研究中，我们分析了在具有永久价格的市场影响模型中竞争流动性的 <i>n</i> 个风险规避代理之间的市场影响博弈影响和额外的滑点。大多数市场参数，包括波动性和漂移，都允许随机变化。我们的第一个主要结果用完全耦合的正反向随机微分方程 (FBSDE) 系统来表征纳什均衡。我们的第二个主要结果提供了该 FBSDE 系统具有唯一解的条件，从而导致唯一的纳什均衡。</p>