Advanced Search
MyIDEAS: Login to save this paper or follow this series

Piecewise deterministic optimal control problems


Author Info

  • Seierstad, Atle

    (Dept. of Economics, University of Oslo)

Registered author(s):


    Piecewise deterministic control problems are problems involving stochastic disturbance of a special type. In certain situations, in an otherwise deterministic control system, it may happen that the state jumps at certain stochastic points of time. Examples are sudden oil finds, or sudden discoveries of metal deposits. Similarly, in seemingly deterministic processes, the dynamics may suddenly change character: at certain stochastic points in time, the right-hand side of the differential equation governing the system changes form, such changes being effected by jumps in a (dummy) state variable. Examples of such phenomena are sudden inventions, sudden ecological disasters, earthquakes, floods, storms, fires, the sudden capture of a criminal, that suddenly change the prospects of the firm, the society, the agriculture, the criminal... Several papers have discussed such problems, often using more or less ad hoc methods. (Sometimes it is possible to rewrite the problem so that deterministic control theory applies). A systematic method for solving such problems, based on HJB-equation (the Hamilton-Jacoby-Bellman equation) for the problem, is presented in Davis (1993). "Markov Models and Optimization", and also briefly discussed below. In this paper a related method, closer to deterministic control theory, is presented first. It is easiest to apply to problems with a bound on the number of possible jumps. Thus, the main purpose of this paper is to show how some piecewise deterministic optimal control problems can be solved by techniques similar to those used in deterministic problems. The paper includes statements of several theoretical results. Proofs are given for the results involving the HJB-equation and fields of extremals, (for the HJB-equation, replicating the ones in Davis (1993)).

    Download Info

    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: no

    Bibliographic Info

    Paper provided by Oslo University, Department of Economics in its series Memorandum with number 39/2003.

    as in new window
    Length: 86 pages
    Date of creation: 01 Dec 2003
    Date of revision:
    Handle: RePEc:hhs:osloec:2003_039

    Contact details of provider:
    Postal: Department of Economics, University of Oslo, P.O Box 1095 Blindern, N-0317 Oslo, Norway
    Phone: 22 85 51 27
    Fax: 22 85 50 35
    Web page:
    More information through EDIRC

    Related research

    Keywords: Stochastic disturbance; deterministic control theory; differential equation;

    Find related papers by JEL classification:


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


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

    Cited by:
    1. Naevdal, Eric, 2006. "Dynamic optimisation in the presence of threshold effects when the location of the threshold is uncertain - with an application to a possible disintegration of the Western Antarctic Ice Sheet," Journal of Economic Dynamics and Control, Elsevier, vol. 30(7), pages 1131-1158, July.


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


    Access and download statistics


    When requesting a correction, please mention this item's handle: RePEc:hhs:osloec:2003_039. 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: (Rhiana Bergh-Seeley).

    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.