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Dynkin games with incomplete and asymmetric information

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  • Tiziano De Angelis
  • Erik Ekstrom
  • Kristoffer Glover

Abstract

We study the value and the optimal strategies for a two-player zero-sum optimal stopping game with incomplete and asymmetric information. In our Bayesian set-up, the drift of the underlying diffusion process is unknown to one player (incomplete information feature), but known to the other one (asymmetric information feature). We formulate the problem and reduce it to a fully Markovian setup where the uninformed player optimises over stopping times and the informed one uses randomised stopping times in order to hide their informational advantage. Then we provide a general verification result which allows us to find the value of the game and players' optimal strategies by solving suitable quasi-variational inequalities with some non-standard constraints. Finally, we study an example with linear payoffs, in which an explicit solution of the corresponding quasi-variational inequalities can be obtained.

Suggested Citation

  • Tiziano De Angelis & Erik Ekstrom & Kristoffer Glover, 2018. "Dynkin games with incomplete and asymmetric information," Papers 1810.07674, arXiv.org, revised Jul 2020.
    • Handle: RePEc:arx:papers:1810.07674
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    File URL: http://arxiv.org/pdf/1810.07674
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    References listed on IDEAS

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    1. Lakner, Peter, 1995. "Utility maximization with partial information," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 247-273, April.
    2. Tiziano De Angelis & Fabien Gensbittel & St'ephane Villeneuve, 2017. "A Dynkin game on assets with incomplete information on the return," Papers 1705.07352, arXiv.org, revised May 2019.
    3. Touzi, N. & Vieille, N., 1999. "Continuous-Time Dynkin Games with Mixed Strategies," Papiers d'Economie Mathématique et Applications 1999.112, Université Panthéon-Sorbonne (Paris 1).
    4. Bing Lu, 2013. "Optimal Selling of an Asset with Jumps Under Incomplete Information," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(6), pages 599-610, December.
    5. Rida Laraki & Eilon Solan, 2002. "Stopping Games in Continuous Time," Discussion Papers 1354, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. Lakner, Peter, 1998. "Optimal trading strategy for an investor: the case of partial information," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 77-97, August.
    7. Fabien Gensbittel & Christine Grün, 2019. "Zero-Sum Stopping Games with Asymmetric Information," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 277-302, February.
    8. Pavel V. Gapeev, 2012. "Pricing Of Perpetual American Options In A Model With Partial Information," World Scientific Book Chapters, in: Matheus R Grasselli & Lane P Hughston (ed.),Finance at Fields, chapter 14, pages 327-347, World Scientific Publishing Co. Pte. Ltd..
    9. repec:dau:papers:123456789/6927 is not listed on IDEAS
    10. Décamps, Jean-Paul & Villeneuve, Stéphane, 2015. "Integrating profitability prospects and cash management," IDEI Working Papers 849, Institut d'Économie Industrielle (IDEI), Toulouse.
    11. Jean-Paul Décamps & Thomas Mariotti & Stéphane Villeneuve, 2005. "Investment Timing Under Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 472-500, May.
    12. Pavel V. Gapeev, 2012. "Pricing Of Perpetual American Options In A Model With Partial Information," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-21.
    13. Brendan Daley & Brett Green, 2012. "Waiting for News in the Market for Lemons," Econometrica, Econometric Society, vol. 80(4), pages 1433-1504, July.
    14. Marta Leniec & Kristoffer Glover & Erik Ekström, 2017. "Dynkin games with heterogeneous beliefs," Published Paper Series 2017-2, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    15. Tomas Björk & Mark Davis & Camilla Landén, 2010. "Optimal investment under partial information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(2), pages 371-399, April.
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    Cited by:

    1. Egor Starkov, 2020. "Only Time Will Tell: Credible Dynamic Signaling," Discussion Papers 20-05, University of Copenhagen. Department of Economics.
    2. Tiziano De Angelis & Nikita Merkulov & Jan Palczewski, 2020. "On the value of non-Markovian Dynkin games with partial and asymmetric information," Papers 2007.10643, arXiv.org.
    3. Tiziano De Angelis & Erik Ekstrom, 2019. "Playing with ghosts in a Dynkin game," Papers 1905.06564, arXiv.org.

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