论文标题
最佳执行情况，具有乘法价格影响和退货的不完整信息
Optimal Execution with Multiplicative Price Impact and Incomplete Information on the Return
论文作者
论文摘要
我们研究了一个最佳的清算问题，并具有乘法价格影响，在这种情况下，资产价格的趋势是无法观察到的Bernoulli随机变量。投资者旨在出售无限的时间疗法固定数量的资产，以最大程度地提高预期利润功能，并允许一次性和奇异的连续行动。我们的数学建模导致一个奇异的随机控制问题，具有有限的燃料约束和部分观察。我们在完整信息下提供了同等的三维退化问题的完整分析，该信息由资产的价格动态，投资组合中的可用资产数量以及投资者对资产趋势的真实价值的信念组成。最佳执行规则和问题的价值函数是根据对真正二维最佳停止问题的解决方案表示的，该问题与信念相关的自由边界$ b $触发了投资者的最佳销售规则。曲线$ b $是通过非线性积分方程式确定的，我们通过蒙特卡洛方法的应用得出数值解决方案。这使我们能够了解问题解决方案对相关模型参数的敏感性以及我们模型中信息的价值。
We study an optimal liquidation problem with multiplicative price impact in which the trend of the asset's price is an unobservable Bernoulli random variable. The investor aims at selling over an infinite time-horizon a fixed amount of assets in order to maximize a net expected profit functional, and lump-sum as well as singularly continuous actions are allowed. Our mathematical modelling leads to a singular stochastic control problem featuring a finite-fuel constraint and partial observation. We provide the complete analysis of an equivalent three-dimensional degenerate problem under full information, whose state process is composed of the asset's price dynamics, the amount of available assets in the portfolio, and the investor's belief about the true value of the asset's trend. The optimal execution rule and the problem's value function are expressed in terms of the solution to a truly two-dimensional optimal stopping problem, whose associated belief-dependent free boundary $b$ triggers the investor's optimal selling rule. The curve $b$ is uniquely determined through a nonlinear integral equation, for which we derive a numerical solution through an application of the Monte-Carlo method. This allows us to understand the sensitivity of the problem's solution with respect to the relevant model's parameters as well as the value of information in our model.
