标题： 弗雷德霍姆方法在非线性传播器模型中的应用 显示英文标题

标题： Fredholm Approach to Nonlinear Propagator Models

摘要： 我们研究了一个带有alpha信号的最佳交易问题，其中交易引起由广义传播者模型描述的非线性瞬时价格影响，包括幂律衰减。使用变分方法，我们证明了最优交易策略满足一个具有前向和后向系数的非线性随机弗雷德霍姆方程。我们在反映价格影响非线性的单调性条件下证明了解的存在性和唯一性。此外，当基础概率空间是可数的时，我们在该条件之外推导出最优策略的存在性结果。另外，我们引入了一种新的迭代方案，并建立了其收敛到最优交易策略的结果。最后，我们提供了该方案的数值实现，展示了其收敛性、稳定性以及在指数衰减和幂律衰减下最优执行策略的凹性效应。 显示英文摘要

摘要： We formulate and solve an optimal trading problem with alpha signals, where transactions induce a nonlinear transient price impact described by a general propagator model, including power-law decay. Using a variational approach, we demonstrate that the optimal trading strategy satisfies a nonlinear stochastic Fredholm equation with both forward and backward coefficients. We prove the existence and uniqueness of the solution under a monotonicity condition reflecting the nonlinearity of the price impact. Moreover, we derive an existence result for the optimal strategy beyond this condition when the underlying probability space is countable. In addition, we introduce a novel iterative scheme and establish its convergence to the optimal trading strategy. Finally, we provide a numerical implementation of the scheme that illustrates its convergence, stability, and the effects of concavity on optimal execution strategies under exponential and power-law decay.