IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v77y2013i2p207-226.html
   My bibliography  Save this article

Optimal decision under ambiguity for diffusion processes

Author

Listed:
  • Sören 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. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:77:y:2013:i:2:p:207-226
    DOI: 10.1007/s00186-012-0425-2
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-012-0425-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-012-0425-2?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. Erik Ekstrom & Stephane Villeneuve, 2006. "On the value of optimal stopping games," Papers math/0610324, arXiv.org.
    7. 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.
    8. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    9. Yuri Kifer, 2000. "Game options," Finance and Stochastics, Springer, vol. 4(4), pages 443-463.
    10. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-436.
    11. Dayanik, Savas & Karatzas, Ioannis, 2003. "On the optimal stopping problem for one-dimensional diffusions," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 173-212, October.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Francesca Biagini & Andrea Mazzon & Katharina Oberpriller, 2023. "Multi-dimensional fractional Brownian motion in the G-setting," Papers 2312.12139, arXiv.org, revised Nov 2024.
    2. Alvarez E., Luis H.R. & Lempa, Jukka & Saarinen, Harto & Sillanpää, Wiljami, 2024. "Solutions for Poissonian stopping problems of linear diffusions via extremal processes," Stochastic Processes and their Applications, Elsevier, vol. 172(C).
    3. 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.
    4. Soren Christensen & Luis H. R. Alvarez E, 2019. "A Solvable Two-dimensional Optimal Stopping Problem in the Presence of Ambiguity," Papers 1905.05429, arXiv.org.
    5. 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.

    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. Soren Christensen, 2011. "Optimal decision under ambiguity for diffusion processes," Papers 1110.3897, arXiv.org, revised Oct 2012.
    2. Vorbrink, Jörg, 2014. "Financial markets with volatility uncertainty," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 64-78.
    3. Paul Viefers, 2012. "Should I Stay or Should I Go?: A Laboratory Analysis of Investment Opportunities under Ambiguity," Discussion Papers of DIW Berlin 1228, DIW Berlin, German Institute for Economic Research.
    4. Volker Krätschmer & Marcel Ladkau & Roger J. A. Laeven & John G. M. Schoenmakers & Mitja Stadje, 2018. "Optimal Stopping Under Uncertainty in Drift and Jump Intensity," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1177-1209, November.
    5. Isaac Kleshchelski & Nicolas Vincent, 2007. "Robust Equilibrium Yield Curves," Cahiers de recherche 08-02, HEC Montréal, Institut d'économie appliquée.
    6. Katia Colaneri & Tiziano De Angelis, 2019. "A class of recursive optimal stopping problems with applications to stock trading," Papers 1905.02650, arXiv.org, revised Jun 2021.
    7. Jianjun Miao, 2009. "Ambiguity, Risk and Portfolio Choice under Incomplete Information," Annals of Economics and Finance, Society for AEF, vol. 10(2), pages 257-279, November.
    8. Carole Bernard & Shaolin Ji & Weidong Tian, 2013. "An optimal insurance design problem under Knightian uncertainty," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 36(2), pages 99-124, November.
    9. Stan Olijslagers & Sweder van Wijnbergen, 2019. "Discounting the Future: on Climate Change, Ambiguity Aversion and Epstein-Zin Preferences," Tinbergen Institute Discussion Papers 19-030/VI, Tinbergen Institute.
    10. Massimo Guidolin & Francesca Rinaldi, 2013. "Ambiguity in asset pricing and portfolio choice: a review of the literature," Theory and Decision, Springer, vol. 74(2), pages 183-217, February.
    11. Bellini, Fabio & Laeven, Roger J.A. & Rosazza Gianin, Emanuela, 2021. "Dynamic robust Orlicz premia and Haezendonck–Goovaerts risk measures," European Journal of Operational Research, Elsevier, vol. 291(2), pages 438-446.
    12. Epstein, Larry G. & Ji, Shaolin, 2014. "Ambiguous volatility, possibility and utility in continuous time," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 269-282.
    13. Szőke, Bálint, 2022. "Estimating robustness," Journal of Economic Theory, Elsevier, vol. 199(C).
    14. A. Jobert & L. C. G. Rogers, 2008. "Valuations And Dynamic Convex Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 1-22, January.
    15. Berend Roorda & J. M. Schumacher & Jacob Engwerda, 2005. "Coherent Acceptability Measures In Multiperiod Models," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 589-612, October.
    16. 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).
    17. Epstein, Larry G. & Miao, Jianjun, 2003. "A two-person dynamic equilibrium under ambiguity," Journal of Economic Dynamics and Control, Elsevier, vol. 27(7), pages 1253-1288, May.
    18. Shi, Zhan, 2019. "Time-varying ambiguity, credit spreads, and the levered equity premium," Journal of Financial Economics, Elsevier, vol. 134(3), pages 617-646.
    19. Jérôme Detemple & Weidong Tian & Jie Xiong, 2012. "An optimal stopping problem with a reward constraint," Finance and Stochastics, Springer, vol. 16(3), pages 423-448, July.
    20. Jeong, Daehee & Kim, Hwagyun & Park, Joon Y., 2015. "Does ambiguity matter? Estimating asset pricing models with a multiple-priors recursive utility," Journal of Financial Economics, Elsevier, vol. 115(2), pages 361-382.

    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:spr:mathme:v:77:y:2013:i:2:p:207-226. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.