IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1110.3897.html
   My bibliography  Save this paper

Optimal decision under ambiguity for diffusion processes

Author

Listed:
  • Soren Christensen

Abstract

In this paper we consider stochastic optimization problems for an ambiguity averse decision maker who is uncertain about the parameters of the underlying process. In a first part we consider problems of optimal stopping under drift ambiguity for one-dimensional diffusion processes. Analogously to the case of ordinary optimal stopping problems for one-dimensional Brownian motions we reduce the problem to the geometric problem of finding the smallest majorant of the reward function in a two-parameter function space. In a second part we solve optimal stopping problems when the underlying process may crash down. These problems are reduced to one optimal stopping problem and one Dynkin game. Examples are discussed.

Suggested Citation

  • Soren Christensen, 2011. "Optimal decision under ambiguity for diffusion processes," Papers 1110.3897, arXiv.org, revised Oct 2012.
    • Handle: RePEc:arx:papers:1110.3897
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1110.3897
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Frank Riedel, 2009. "Optimal Stopping With Multiple Priors," Econometrica, Econometric Society, vol. 77(3), pages 857-908, May.
    2. Riedel, Frank, 2010. "Optimal Stopping under Ambiguity in Continuous Time," Center for Mathematical Economics Working Papers 429, Center for Mathematical Economics, Bielefeld University.
    3. Tatjana Chudjakow & Frank Riedel, 2013. "The best choice problem under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 77-97, September.
    4. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    5. Riedel, Frank, 2010. "Optimal Stopping under Ambiguity," Center for Mathematical Economics Working Papers 390, Center for Mathematical Economics, Bielefeld University.
    6. Soren Christensen, 2011. "A method for pricing American options using semi-infinite linear programming," Papers 1103.4483, arXiv.org, revised Jun 2011.
    7. Erik Ekstrom & Stephane Villeneuve, 2006. "On the value of optimal stopping games," Papers math/0610324, arXiv.org.
    8. Stéphane Villeneuve & Erik Ekstrom, 2006. "On the Value of Optimal Stopping Games," Post-Print hal-00173182, HAL.
    9. Luis H. R. Alvarez E., 2006. "A Class of Solvable Stopping Games," Discussion Papers 11, Aboa Centre for Economics.
    10. Ralf Korn & Paul Wilmott, 2002. "Optimal Portfolios Under The Threat Of A Crash," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 171-187.
    11. Yuri Kifer, 2000. "Game options," Finance and Stochastics, Springer, vol. 4(4), pages 443-463.
    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. Sören Christensen, 2013. "Optimal decision under ambiguity for diffusion processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(2), pages 207-226, April.
    2. Vorbrink, Jörg, 2014. "Financial markets with volatility uncertainty," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 64-78.
    3. Yuri Kifer, 2012. "Dynkin Games and Israeli Options," Papers 1209.1791, arXiv.org.
    4. repec:diw:diwwpp:dp1228 is not listed on IDEAS
    5. Yan Dolinsky & Ariel Neufeld, 2015. "Super-replication in Fully Incomplete Markets," Papers 1508.05233, arXiv.org, revised Sep 2016.
    6. Luis H. R. Alvarez E., 2006. "Minimum Guaranteed Payments and Costly Cancellation Rights: A Stopping Game Perspective," Discussion Papers 12, Aboa Centre for Economics.
    7. Boyarchenko, Svetlana & Levendorskiĭ, Sergei, 2014. "Preemption games under Lévy uncertainty," Games and Economic Behavior, Elsevier, vol. 88(C), pages 354-380.
    8. De Angelis, Tiziano & Gensbittel, Fabien & Villeneuve, Stéphane, 2017. "A Dynkin game on assets with incomplete information on the return," TSE Working Papers 17-815, Toulouse School of Economics (TSE).
    9. Patrick Beissner, 2019. "Coherent-Price Systems and Uncertainty-Neutral Valuation," Risks, MDPI, vol. 7(3), pages 1-18, September.
    10. 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, revised Feb 2021.
    11. Dana, Rose-Anne & Riedel, Frank, 2013. "Intertemporal equilibria with Knightian uncertainty," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1582-1605.
    12. Gonçalo Faria & João Correia-da-Silva, 2012. "The price of risk and ambiguity in an intertemporal general equilibrium model of asset prices," Annals of Finance, Springer, vol. 8(4), pages 507-531, November.
    13. repec:ipg:wpaper:16 is not listed on IDEAS
    14. Luis H. R. Alvarez E. & Paavo Salminen, 2017. "Timing in the presence of directional predictability: optimal stopping of skew Brownian motion," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(2), pages 377-400, October.
    15. Gonçalo Faria & João Correia-da-Silva, 2014. "A closed-form solution for options with ambiguity about stochastic volatility," Review of Derivatives Research, Springer, vol. 17(2), pages 125-159, July.
    16. Farzad Pourbabaee, 2022. "Robust experimentation in the continuous time bandit problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(1), pages 151-181, February.
    17. Saghafian, Soroush, 2018. "Ambiguous partially observable Markov decision processes: Structural results and applications," Journal of Economic Theory, Elsevier, vol. 178(C), pages 1-35.
    18. Tatjana Chudjakow & Frank Riedel, 2013. "The best choice problem under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 77-97, September.
    19. repec:diw:diwwpp:dp1401 is not listed on IDEAS
    20. Garlappi, Lorenzo & Giammarino, Ron & Lazrak, Ali, 2017. "Ambiguity and the corporation: Group disagreement and underinvestment," Journal of Financial Economics, Elsevier, vol. 125(3), pages 417-433.
    21. Luis H. R. Alvarez E. & Soren Christensen, 2019. "A Class of Solvable Multidimensional Stopping Problems in the Presence of Knightian Uncertainty," Papers 1907.04046, arXiv.org.
    22. Kishishita, Daiki, 2020. "(Not) delegating decisions to experts: The effect of uncertainty," Journal of Economic Theory, Elsevier, vol. 190(C).
    23. Luis H. R. Alvarez E. & Soren Christensen, 2019. "The Impact of Ambiguity on the Optimal Exercise Timing of Integral Option Contracts," Papers 1906.07533, arXiv.org.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:1110.3897. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.