IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this article

Mean--Variance Optimal Adaptive Execution

Listed author(s):
  • Julian Lorenz
  • Robert Almgren
Registered author(s):

    Electronic trading of equities and other securities makes heavy use of ‘arrival price’ algorithms that balance the market impact cost of rapid execution against the volatility risk of slow execution. In the standard formulation, mean--variance optimal trading strategies are static: they do not modify the execution speed in response to price motions observed during trading. We show that substantial improvement is possible by using dynamic trading strategies and that the improvement is larger for large initial positions. We develop a technique for computing optimal dynamic strategies to any desired degree of precision. The asset price process is observed on a discrete tree with an arbitrary number of levels. We introduce a novel dynamic programming technique in which the control variables are not only the shares traded at each time step but also the maximum expected cost for the remainder of the program; the value function is the variance of the remaining program. The resulting adaptive strategies are ‘aggressive-in-the-money’: they accelerate the execution when the price moves in the trader's favor, spending parts of the trading gains to reduce risk.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 18 (2011)
    Issue (Month): 5 (January)
    Pages: 395-422

    in new window

    Handle: RePEc:taf:apmtfi:v:18:y:2011:i:5:p:395-422
    DOI: 10.1080/1350486X.2011.560707
    Contact details of provider: Web page:

    Order Information: Web:

    No references listed on IDEAS
    You can help add them by filling out this form.

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:taf:apmtfi:v:18:y:2011:i:5:p:395-422. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Chris Longhurst)

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.