在市场阻力和凹状价格影响下进行交易
Trading with market resistance and concave price impact
AI总结：
本文提出了一种考虑内生市场阻力和凹状价格影响的最优交易模型，并通过数学分析和数值实验验证了最优交易策略的存在性和收敛性。
摘要：
我们考虑了一个在具有内生市场阻力的市场影响模型下的最优交易问题，该模型由一个精明的交易者生成，该交易者（部分）检测到元订单并与其交易以利用由订单流引起的价格过度反应。该模型的特点是由幂律传播器驱动的凹暂时影响，其阻力项通过涉及一般阻力函数的固定点方程对交易者的速率作出响应。我们推导出一个（非）线性随机Fredholm方程作为最优交易策略所满足的一阶最优性条件。当阻力函数为线性时，建立了最优控制的存在性和唯一性；当其为严格凸时，利用 coercivity 和弱下半连续性得到了存在性结果。我们还提出了一种迭代方案来求解非线性随机Fredholm方程，并证明了指数收敛率。数值实验验证了这种行为，并展示了在“买入”信号下，具有不同衰减曲线和不同市场阻力规格的最优往返策略。
英文摘要：
We consider an optimal trading problem under a market impact model with endogenous market resistance generated by a sophisticated trader who (partially) detects metaorders and trades against them to exploit price overreactions induced by the order flow. The model features a concave transient impact driven by a power-law propagator with a resistance term responding to the trader's rate via a fixed-point equation involving a general resistance function. We derive a (non)linear stochastic Fredholm equation as the first-order optimality condition satisfied by optimal trading strategies. Existence and uniqueness of the optimal control are established when the resistance function is linear, and an existence result is obtained when it is strictly convex using coercivity and weak lower semicontinuity of the associated profit-and-loss functional. We also propose an iterative scheme to solve the nonlinear stochastic Fredholm equation and prove an exponential convergence rate. Numerical experiments confirm this behavior and illustrate optimal round-trip strategies under "buy" signals with various decay profiles and different market resistance specifications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
