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摘要翻译：
假设几何布朗运动是不受影响的价格过程$S^0$，Gatheral&Schied(2011)导出了一个最优订单执行策略，该策略对市场变化有合理的反应，但仍然可以用封闭的形式计算。在这里，我们将研究此策略对于$S^0$定律的错误说明的鲁棒性。我们证明了当$S^0$是平方可积鞅时，该策略保持最优的惊人结果。然后分析了Gatheral&Schied(2011)在$S^0$为任意平方可积半鞅的情况下的优化准则，并给出了该问题的闭式解。作为推论，当不受影响的价格过程为平方可积半鞅时，我们找到了期望清算成本最小化问题的显式解。我们的问题的解是通过随机求解一个有限燃料控制问题而不假设马尔可夫性来找到的。
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英文标题：
《Robust Strategies for Optimal Order Execution in the Almgren-Chriss
Framework》
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作者：
Alexander Schied
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最新提交年份：
2013
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Trading and Market Microstructure 交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
Assuming geometric Brownian motion as unaffected price process $S^0$, Gatheral & Schied (2011) derived a strategy for optimal order execution that reacts in a sensible manner on market changes but can still be computed in closed form. Here we will investigate the robustness of this strategy with respect to misspecification of the law of $S^0$. We prove the surprising result that the strategy remains optimal whenever $S^0$ is a square-integrable martingale. We then analyze the optimization criterion of Gatheral & Schied (2011) in the case in which $S^0$ is any square-integrable semimartingale and we give a closed-form solution to this problem. As a corollary, we find an explicit solution to the problem of minimizing the expected liquidation costs when the unaffected price process is a square-integrable semimartingale. The solutions to our problems are found by stochastically solving a finite-fuel control problem without assumptions of Markovianity.
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PDF链接：
https://arxiv.org/pdf/1204.2717
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