IDEAS home Printed from https://ideas.repec.org/a/spr/comgts/v3y2006i1p81-100.html
   My bibliography  Save this article

Optimal impulse control on an unbounded domain with nonlinear cost functions

Author

Listed:
  • Stefano Baccarin
  • Simona Sanfelici

Abstract

In this paper we consider the optimal impulse control of a system which evolves randomly in accordance with a homogeneous diffusion process in ℜ 1 . Whenever the system is controlled a cost is incurred which has a fixed component and a component which increases with the magnitude of the control applied. In addition to these controlling costs there are holding or carrying costs which are a positive function of the state of the system. Our objective is to minimize the expected discounted value of all costs over an infinite planning horizon. Under general assumptions on the cost functions we show that the value function is a weak solution of a quasi-variational inequality and we deduce from this solution the existence of an optimal impulse policy. The computation of the value function is performed by means of the Finite Element Method on suitable truncated domains, whose convergence is discussed. Copyright Springer-Verlag Berlin/Heidelberg 2006

Suggested Citation

  • Stefano Baccarin & Simona Sanfelici, 2006. "Optimal impulse control on an unbounded domain with nonlinear cost functions," Computational Management Science, Springer, vol. 3(1), pages 81-100, January.
    • Handle: RePEc:spr:comgts:v:3:y:2006:i:1:p:81-100
    DOI: 10.1007/s10287-005-0045-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10287-005-0045-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10287-005-0045-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

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


    Cited by:

    1. Baccarin, Stefano, 2009. "Optimal impulse control for a multidimensional cash management system with generalized cost functions," European Journal of Operational Research, Elsevier, vol. 196(1), pages 198-206, July.
    2. Korn, Ralf & Melnyk, Yaroslav & Seifried, Frank Thomas, 2017. "Stochastic impulse control with regime-switching dynamics," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1024-1042.
    3. Ibtissam Hdhiri & Monia Karouf, 2011. "Risk sensitive impulse control of non-Markovian processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(1), pages 1-20, August.

    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:spr:comgts:v:3:y:2006:i:1:p:81-100. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.