Drift dependence of optimal trade execution strategies under transient price impact
Drift dependence of optimal trade execution strategies under transient price impact
复制标题
DOI：
10.2139/ssrn.1993103
复制
发表时间：
2012-04
影响因子：
1.7
通讯作者：
C. Lorenz;A. Schied
中科院分区：
文献类型：
--
作者：
C. Lorenz;A. Schied
我们给出了当标的市场影响模型具有指数弹性的线性瞬时价格影响时，在存在一般漂移的情况下最小化预期流动性成本问题的完整解决方案。事实证明，只有当漂移是绝对连续的时，这个问题才是适定的。最优策略通常不存在，当它们存在时，它们强烈地依赖于漂移的导数。我们的方法使用了来自奇异随机控制的元素，尽管由于价格影响的瞬变和基础价格过程的马尔可夫结构的缺乏，问题本质上是非马尔可夫的。作为推论，我们给出了在我们的设置下最小化某一成本-风险准则的完整解决方案。
We give a complete solution to the problem of minimizing the expected liquidity costs in the presence of a general drift when the underlying market impact model has linear transient price impact with exponential resilience. It turns out that this problem is well-posed only if the drift is absolutely continuous. Optimal strategies often do not exist, and when they do, they depend strongly on the derivative of the drift. Our approach uses elements from singular stochastic control, even though the problem is essentially non-Markovian due to the transience of price impact and the lack in Markovian structure of the underlying price process. As a corollary, we give a complete solution to the minimization of a certain cost-risk criterion in our setting.