IDEAS home Printed from https://ideas.repec.org/a/bla/mathfi/v29y2019i1p208-248.html
   My bibliography  Save this article

Backward SDEs for control with partial information

Author

Listed:
  • Andrew Papanicolaou

Abstract

This paper considers a non‐Markov control problem arising in a financial market where asset returns depend on hidden factors. The problem is non‐Markov because nonlinear filtering is required to make inference on these factors, and hence the associated dynamic program effectively takes the filtering distribution as one of its state variables. This is of significant difficulty because the filtering distribution is a stochastic probability measure of infinite dimension, and therefore the dynamic program has a state that cannot be differentiated in the traditional sense. This lack of differentiability means that the problem cannot be solved using a Hamilton–Jacobi–Bellman equation. This paper will show how the problem can be analyzed and solved using backward stochastic differential equations, with a key tool being the problem's dual formulation.

Suggested Citation

  • Andrew Papanicolaou, 2019. "Backward SDEs for control with partial information," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 208-248, January.
    • Handle: RePEc:bla:mathfi:v:29:y:2019:i:1:p:208-248
    DOI: 10.1111/mafi.12174
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/mafi.12174
    Download Restriction: no
    File URL: https://libkey.io/10.1111/mafi.12174?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
    ---><---

    Citations

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


    Cited by:

    1. Dongmei Zhu & Harry Zheng, 2022. "Effective Approximation Methods for Constrained Utility Maximization with Drift Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 191-219, July.
    2. Chao Deng & Xizhi Su & Chao Zhou, 2020. "Relative wealth concerns with partial information and heterogeneous priors," Papers 2007.11781, arXiv.org.
    3. Sebastian Jaimungal & Xiaofei Shi, 2024. "The Price of Information," Papers 2402.11864, arXiv.org, revised Mar 2024.
    4. Claudia Ceci & Alessandra Cretarola, 2024. "Optimal reinsurance in a dynamic contagion model: comparing self-exciting and externally-exciting risks," Papers 2404.11482, arXiv.org, revised Sep 2024.
    5. Elisabeth Leoff & Leonie Ruderer & Jörn Sass, 2022. "Signal-to-noise matrix and model reduction in continuous-time hidden Markov models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(2), pages 327-359, April.

    More about this item

    Statistics

    Access and download statistics

    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:bla:mathfi:v:29:y:2019:i:1:p:208-248. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627 .

    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.