IDEAS home Printed from https://ideas.repec.org/a/inm/ormoor/v48y2023i3p1657-1678.html
   My bibliography  Save this article

Risk-Averse Optimal Control in Continuous Time by Nesting Risk Measures

Author

Listed:
  • Alois Pichler

    (Faculty of Mathematics, Chemnitz University of Technology, 09111 Chemnitz, Germany)

  • Ruben Schlotter

    (Faculty of Mathematics, Chemnitz University of Technology, 09111 Chemnitz, Germany)

Abstract

This paper extends dynamic control problems from a risk-neutral to a risk-averse setting. We establish a limit for consecutive risk-averse decision making by consistently and adequately nesting coherent risk measures. This approach provides a new perspective on multistage optimal control problems in continuous time. For the limiting case, we elaborate a new dynamic programming principle, which is risk averse, and give risk-averse Hamilton–Jacobi–Bellman equations by generalizing the infinitesimal generator. In doing so, we provide a constructive explanation of the driver g in g -expectation, a dynamic risk measure based on backward stochastic differential equations.

Suggested Citation

  • Alois Pichler & Ruben Schlotter, 2023. "Risk-Averse Optimal Control in Continuous Time by Nesting Risk Measures," Mathematics of Operations Research, INFORMS, vol. 48(3), pages 1657-1678, August.
    • Handle: RePEc:inm:ormoor:v:48:y:2023:i:3:p:1657-1678
    DOI: 10.1287/moor.2022.1314
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/moor.2022.1314
    Download Restriction: no
    File URL: https://libkey.io/10.1287/moor.2022.1314?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
    ---><---

    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:inm:ormoor:v:48:y:2023:i:3:p:1657-1678. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.