IDEAS home Printed from https://ideas.repec.org/p/bie/wpaper/721.html

Stochastic representation under g-expectation and applications: The discrete time case

Author

Listed:
  • Grigorova, Miryana

    (Center for Mathematical Economics, Bielefeld University)

  • Li, Hanwu

    (Center for Mathematical Economics, Bielefeld University)

Abstract

In this paper, we address the stochastic representation problem in discrete time under (non-linear) g-expectation. We establish existence and uniqueness of the solution, as well as a characterization of the solution. As an application, we investigate a new approach to the optimal stopping problem under g-expectation and the related pricing of American options under Knightian uncertainty. Our results are also applied to a (non-linear) Skorokhod-type obstacle problem.

Suggested Citation

  • Grigorova, Miryana & Li, Hanwu, 2025. "Stochastic representation under g-expectation and applications: The discrete time case," Center for Mathematical Economics Working Papers 721, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:721
    as

    Download full text from publisher

    File URL: https://pub.uni-bielefeld.de/download/3005284/3005285
    File Function: First Version, 2022
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Patrick Beissner & Qian Lin & Frank Riedel, 2020. "Dynamically consistent alpha‐maxmin expected utility," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 1073-1102, July.
    2. Frank Riedel & Xia Su, 2011. "On irreversible investment," Finance and Stochastics, Springer, vol. 15(4), pages 607-633, December.
    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. de Angelis, Tiziano & Ferrari, Giorgio, 2014. "A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis," Center for Mathematical Economics Working Papers 477, Center for Mathematical Economics, Bielefeld University.
    2. Maria B. Chiarolla & Giorgio Ferrari & Frank Riedel, 2012. "Generalized Kuhn-Tucker Conditions for N-Firm Stochastic Irreversible Investment under Limited Resources," Papers 1203.3757, arXiv.org, revised Aug 2013.
    3. Keisuke Kizaki & Taiga Saito & Akihiko Takahashi, 2023. "Equilibriummulti-agent model with heterogeneous views on fundamental risks (Forthcoming in Automatica)," CARF F-Series CARF-F-571, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    4. Giorgio Ferrari & Hanwu Li & Frank Riedel, 2020. "A Knightian Irreversible Investment Problem," Papers 2003.14359, arXiv.org, revised Apr 2020.
    5. Drugeon, Jean-Pierre & Ha-Huy, Thai, 2021. "An $\alpha-$MaxMin Axiomatisation of Temporally-Biased Multiple Discounts," MPRA Paper 111306, University Library of Munich, Germany.
    6. Jan-Henrik Steg, 2024. "Strategic Irreversible Investment," Papers 2410.17673, arXiv.org.
    7. Alain Bensoussan & Benoît Chevalier-Roignant, 2019. "Sequential Capacity Expansion Options," Operations Research, INFORMS, vol. 67(1), pages 33-57, January.
    8. Ferrari, Giorgio & Riedel, Frank & Steg, Jan-Henrik, 2016. "Continuous-Time Public Good Contribution under Uncertainty," Center for Mathematical Economics Working Papers 485, Center for Mathematical Economics, Bielefeld University.
    9. Frick, Mira & Iijima, Ryota & Le Yaouanq, Yves, 2022. "Objective rationality foundations for (dynamic) α-MEU," Journal of Economic Theory, Elsevier, vol. 200(C).
    10. Aïd, René & Basei, Matteo & Ferrari, Giorgio, 2023. "A Stationary Mean-Field Equilibrium Model of Irreversible Investment in a Two-Regime Economy," Center for Mathematical Economics Working Papers 679, Center for Mathematical Economics, Bielefeld University.
    11. Hervé Roche, 2022. "The implications of tax loss carryforwards on investment policy," Mathematics and Financial Economics, Springer, volume 16, number 6, March.
    12. Jiacheng Fan & Xue Dong He & Ruocheng Wu, 2025. "Dynamic Asset Pricing with {\alpha}-MEU Model," Papers 2507.04093, arXiv.org, revised Dec 2025.
    13. Mononen, Lasse, 2024. "Dynamically Consistent Intertemporal Dual-Self Expected Utility," Center for Mathematical Economics Working Papers 686, Center for Mathematical Economics, Bielefeld University.
    14. Chiarolla, Maria B. & Ferrari, Giorgio & Stabile, Gabriele, 2015. "Optimal dynamic procurement policies for a storable commodity with Lévy prices and convex holding costs," European Journal of Operational Research, Elsevier, vol. 247(3), pages 847-858.
    15. Ferrari, Giorgio & Salminen, Paavo, 2016. "Irreversible Investment under Lévy Uncertainty: an Equation for the Optimal Boundary," Center for Mathematical Economics Working Papers 530, Center for Mathematical Economics, Bielefeld University.
    16. de Angelis, Tiziano & Federico, Salvatore & Ferrari, Giorgio, 2016. "On the Optimal Boundary of a Three-Dimensional Singular Stochastic Control Problem Arising in Irreversible Investment," Center for Mathematical Economics Working Papers 509, Center for Mathematical Economics, Bielefeld University.
    17. Zhang, Liming & Li, Bin, 2021. "Optimal reinsurance under the α-maxmin mean-variance criterion," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 225-239.
    18. Peter Bank & David Besslich, 2018. "Modelling information flows by Meyer-$\sigma$-fields in the singular stochastic control problem of irreversible investment," Papers 1810.08495, arXiv.org, revised Mar 2020.
    19. Shuang Li & Haijun Wang, 2023. "Robust irreversible investment strategy with ambiguity to jump and diffusion risk," International Review of Finance, International Review of Finance Ltd., vol. 23(3), pages 645-665, September.
    20. Ferrari, Giorgio, 2016. "Controlling public debt without forgetting Inflation," Center for Mathematical Economics Working Papers 564, Center for Mathematical Economics, Bielefeld University.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    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:bie:wpaper:721. 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: Bettina Weingarten (email available below). General contact details of provider: https://edirc.repec.org/data/imbiede.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.