摘要翻译：
在Almgren-Chriss框架中，我们导出了目标关闭(TC)和实现不足(IS)的显式递归公式。在给定最小交易规模的情况下，我们解释了如何分别计算IS和TC的最优开始时间和停止时间。我们还展示了如何为TC和IS添加最小参与率约束（体积百分比，PVol)。我们还研究了算法交易曲线优化的另一套风险度量。我们假设一个自相似过程（如Levy过程、分数布朗运动或分形过程），并定义了一个新的风险度量&P变差，当该过程是布朗运动时，它将变差归结为方差。在一个自相似过程下，推导了TC和IS算法的显式公式。我们证明了自相似模型与一族称为p-变差的风险度量之间存在等价性：假设一个自相似过程，并根据经验校准p-变差的参数p，得到的结果与假设布朗运动，并使用p-变差作为风险度量而不是方差相同。我们还证明了p可以被看作是侵略性的度量：当且仅当TC算法开始得更晚且执行得更快时，p才增加。最后，我们证明了p-变差的参数p是如何从TC的最优开始时间来隐含的，并且在此框架下，p可以被看作是市场冲击（即流动性）和波动性的联合影响的度量。
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英文标题：
《Optimal starting times, stopping times and risk measures for algorithmic
  trading: Target Close and Implementation Shortfall》
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作者：
Mauricio Labadie and Charles-Albert Lehalle
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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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英文摘要：
  We derive explicit recursive formulas for Target Close (TC) and Implementation Shortfall (IS) in the Almgren-Chriss framework. We explain how to compute the optimal starting and stopping times for IS and TC, respectively, given a minimum trading size. We also show how to add a minimum participation rate constraint (Percentage of Volume, PVol) for both TC and IS. We also study an alternative set of risk measures for the optimisation of algorithmic trading curves. We assume a self-similar process (e.g. Levy process, fractional Brownian motion or fractal process) and define a new risk measure, the p-variation, which reduces to the variance if the process is a brownian motion. We deduce the explicit formula for the TC and IS algorithms under a self-similar process. We show that there is an equivalence between selfsimilar models and a family of risk measures called p-variations: assuming a self-similar process and calibrating empirically the parameter p for the p-variation yields the same result as assuming a Brownian motion and using the p-variation as risk measure instead of the variance. We also show that p can be seen as a measure of the aggressiveness: p increases if and only if the TC algorithm starts later and executes faster. Finally, we show how the parameter p of the p-variation can be implied from the optimal starting time of TC, and that under this framework p can be viewed as a measure of the joint impact of market impact (i.e. liquidity) and volatility.
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PDF链接：
https://arxiv.org/pdf/1205.3482