IDEAS home Printed from https://ideas.repec.org/p/hal/journl/halshs-00167141.html
   My bibliography  Save this paper

Optimal investment with taxes: an optimal control problem with endogeneous delay

Author

Listed:
  • Elyès Jouini

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Pierre-François Koehl
  • Nizar Touzi

Abstract

Here, we study the case where the portfolio rebalancement involves the payment of taxes on benefits. Then, the purchasing time of the asset to be sold has to be recorded in order to compute the amount of tax to be paid. In addition to the no-short-selling constraint, our model assumes that sales are subject to the first-in-first-out priority rule on sales. A precise description of the model is given in Section 2. The agent problem turns out to be a nonclassical optimal control problem with endogeneous delay andwith complex nonnegativity constraint on consumption. Section 3 is devoted to the proof of the following economic appealing result. An optimal strategy can always be chosen such that the agent never sells out of his portfolio and buy new Financial assets simultaneously. Using this property, the nonnegativity constraint on consumption is simplified and reduced to a classical constraint on the controls and the state variables. Namely, the nonnegativity constraint on consumption can be expressed simply in terms of the investment and the disinvestment functions. In Section 4, we assume some additional smoothness conditions on the optimal strategy in order to derive the first-order conditions associated to the control problem of interest. The usual variational methods are adapted to handle the endogeneous delay function.

Suggested Citation

  • Elyès Jouini & Pierre-François Koehl & Nizar Touzi, 1999. "Optimal investment with taxes: an optimal control problem with endogeneous delay," Post-Print halshs-00167141, HAL.
  • Handle: RePEc:hal:journl:halshs-00167141
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jouini, Elyes & Koehl, Pierre-F. & Touzi, Nizar, 2000. "Optimal investment with taxes: an existence result," Journal of Mathematical Economics, Elsevier, vol. 33(4), pages 373-388, May.
    2. repec:dau:papers:123456789/5600 is not listed on IDEAS
    3. Christoph Kuhn, 2018. "How local in time is the no-arbitrage property under capital gains taxes ?," Papers 1802.06386, arXiv.org, revised Sep 2018.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:halshs-00167141. See general information about how to correct material in RePEc.

    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.

    We have no bibliographic references for this item. You can help adding them by using 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.