IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/inria-00573117.html
   My bibliography  Save this paper

Robust stochastic control and equivalent martingale measures

Author

Listed:
  • Bernt Oksendal

    (CMA - Center of Mathematics for Applications [Oslo] - Department of Mathematics [Oslo] - Faculty of Mathematics and Natural Sciences [Oslo] - UiO - University of Oslo)

  • Agnès Sulem

    (MATHFI - Financial mathematics - Inria Paris-Rocquencourt - Inria - Institut National de Recherche en Informatique et en Automatique - ENPC - École des Ponts ParisTech - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12)

Abstract

We study a class of robust, or worst case scenario, optimal control problems for jump diffusions. The scenario is represented by a probability measure equivalent to the initial probability law. We show that if there exists a control that annihilates the noise coefficients in the state equation and a scenario which is an equivalent martingale measure for a specific process which is related to the control-derivative of the state process, then this control and this probability measure are optimal. We apply the result to the problem of consumption and portfolio optimization under model uncertainty in a financial market, where the price process S(t) of the risky asset is modeled as a geometric Itô-Lévy process. In this case the optimal scenario is an equivalent local martingale measure of S(t). We solve this problem explicitly in the case of logarithmic utility functions.

Suggested Citation

  • Bernt Oksendal & Agnès Sulem, 2011. "Robust stochastic control and equivalent martingale measures," Working Papers inria-00573117, HAL.
    • Handle: RePEc:hal:wpaper:inria-00573117
    Note: View the original document on HAL open archive server: https://inria.hal.science/inria-00573117
    as

    Download full text from publisher

    File URL: https://inria.hal.science/inria-00573117/document
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hansen, Lars Peter & Sargent, Thomas J., 2022. "Structured ambiguity and model misspecification," Journal of Economic Theory, Elsevier, vol. 199(C).
    2. Taiga Saito & Akihiko Takahashi, 2019. "A novel approach to asset pricing with choice of probability measures," CARF F-Series CARF-F-471, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jan 2021.
    3. Karantounias, Anastasios G., 2023. "Doubts about the model and optimal policy," Journal of Economic Theory, Elsevier, vol. 210(C).
    4. Johannes Emmerling & Vassiliki Manoussi & Anastasios Xepapadeas, 2016. "Climate Engineering under Deep Uncertainty and Heterogeneity," Working Papers 2016.52, Fondazione Eni Enrico Mattei.
    5. Itzhak Gilboa & Andrew Postlewaite & Larry Samuelson & David Schmeidler, 2011. "Economic Models as Analogies," PIER Working Paper Archive 12-001, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    6. Alexei Onatski & Noah Williams, 2003. "Modeling Model Uncertainty," Journal of the European Economic Association, MIT Press, vol. 1(5), pages 1087-1122, September.
    7. Souza, Thiago de Oliveira, 2020. "Dollar carry timing," Discussion Papers on Economics 10/2020, University of Southern Denmark, Department of Economics.
    8. Adam – Nelu ALTĂR – SAMUEL, 2008. "Robust Monetary Policy," Journal of Information Systems & Operations Management, Romanian-American University, vol. 2(2), pages 475-486, November.
    9. H. Henry Cao & Bing Han & David Hirshleifer & Harold H. Zhang, 2011. "Fear of the Unknown: Familiarity and Economic Decisions," Review of Finance, European Finance Association, vol. 15(1), pages 173-206.
    10. repec:esx:essedp:770 is not listed on IDEAS
    11. Gérard Mondello, 2022. "Information Source's Reliability," GREDEG Working Papers 2022-21, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France, revised Oct 2022.
    12. Arnulfo Rodriguez, 2004. "Robust Control: A Note on the Timing of Model Uncertainty," Computing in Economics and Finance 2004 147, Society for Computational Economics.
    13. Claudio A. Bonilla & Pablo A. Gutiérrez Cubillos, 2021. "The effects of ambiguity on entrepreneurship," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 30(1), pages 63-80, February.
    14. Junyi Chai & Zhiquan Weng & Wenbin Liu, 2021. "Behavioral Decision Making in Normative and Descriptive Views: A Critical Review of Literature," JRFM, MDPI, vol. 14(10), pages 1-14, October.
    15. Marciano Siniscalchi, 2009. "Vector Expected Utility and Attitudes Toward Variation," Econometrica, Econometric Society, vol. 77(3), pages 801-855, May.
    16. Fu, Qi & So, Jacky Yuk-Chow & Li, Xiaotong, 2024. "Stable paretian distribution, return generating processes and habit formation—The implication for equity premium puzzle," The North American Journal of Economics and Finance, Elsevier, vol. 70(C).
    17. Sosung Baik & Sung-Ha Hwang, 2021. "Auction design with ambiguity: Optimality of the first-price and all-pay auctions," Papers 2110.08563, arXiv.org.
    18. Subhadeep Mukhopadhyay, 2023. "Modelplasticity and abductive decision making," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 255-276, June.
    19. Herzberg, Frederik, 2014. "Aggregation of Monotonic Bernoullian Archimedean preferences: Arrovian impossibility results," Center for Mathematical Economics Working Papers 488, Center for Mathematical Economics, Bielefeld University.
    20. Aït-Sahalia, Yacine & Matthys, Felix, 2019. "Robust consumption and portfolio policies when asset prices can jump," Journal of Economic Theory, Elsevier, vol. 179(C), pages 1-56.
    21. Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2012. "The Appeal of Information Transactions," Working Papers 2012-13, Brown University, Department of Economics.

    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:wpaper:inria-00573117. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc 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 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.