IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v80y2010i11-12p950-957.html
   My bibliography  Save this article

Examples of optimal prediction in the infinite horizon case

Author

Listed:
  • Cohen, Albert

Abstract

Timing of financial decisions, especially in a volatile market such as the one we are in now, is crucial to maintaining and growing wealth. Without premonition or inside information, buyers and sellers of financial assets may experience a form of remorse for selling too late or buying too early. A valuable tool in reducing such regret is an algorithm that tells the asset holder when to sell "optimally". In the case of a Brownian-valued asset, Graversen et al. (2000) proposed the strategy of Optimal Prediction, where the Brownian motion is stopped as close as possible, in the mean-square sense, to its ultimate maximum over the entire term [0,T]. Any candidate for the optimal stopping time must be adapted to the filtration of the underlying asset, since no inside information is to be assumed. Later work, nicely summarized in the book of Peskir and Shiryaev (2006), has extended this field to include different non-adapted functionals and different measures of "closeness". In this article, we seek to extend the field of optimal prediction to the perpetual, or infinite horizon, case. Some examples related to the ultimate risk associated with holding a toxic liability and the ultimately best time to sell a stock are presented, and their closed form solutions are computed.

Suggested Citation

  • Cohen, Albert, 2010. "Examples of optimal prediction in the infinite horizon case," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 950-957, June.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:11-12:p:950-957
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(10)00046-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Jacques du Toit & Goran Peskir, 2009. "Selling a stock at the ultimate maximum," Papers 0908.1014, arXiv.org.
    2. Gerber, Hans U., 1977. "On Optimal Cancellation of Policies," ASTIN Bulletin, Cambridge University Press, vol. 9(1-2), pages 125-138, January.
    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. Peskir, Goran, 2012. "Optimal detection of a hidden target: The median rule," Stochastic Processes and their Applications, Elsevier, vol. 122(5), pages 2249-2263.
    2. M'onica B. Carvajal Pinto & Kees van Schaik, 2019. "Optimally stopping at a given distance from the ultimate supremum of a spectrally negative L\'evy process," Papers 1904.11911, arXiv.org, revised Jul 2020.
    3. Albert Cohen, 2018. "Editorial: A Celebration of the Ties That Bind Us: Connections between Actuarial Science and Mathematical Finance," Risks, MDPI, vol. 6(1), pages 1-3, January.

    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. Johnson, P. & Pedersen, J.L. & Peskir, G. & Zucca, C., 2022. "Detecting the presence of a random drift in Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 1068-1090.
    2. Gunther Leobacher & Michaela Szolgyenyi & Stefan Thonhauser, 2016. "Bayesian Dividend Optimization and Finite Time Ruin Probabilities," Papers 1602.04660, arXiv.org.
    3. Bjarne Højgaard & Michael Taksar, 2004. "Optimal dynamic portfolio selection for a corporation with controllable risk and dividend distribution policy," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 315-327.
    4. Peskir, Goran, 2012. "Optimal detection of a hidden target: The median rule," Stochastic Processes and their Applications, Elsevier, vol. 122(5), pages 2249-2263.
    5. Luluwah Al-Fagih, 2015. "The British Knock-Out Put Option," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 1-32.
    6. Buonaguidi, B., 2023. "An optimal sequential procedure for determining the drift of a Brownian motion among three values," Stochastic Processes and their Applications, Elsevier, vol. 159(C), pages 320-349.
    7. Arcand, Jean-Louis & Hongler, Max-Olivier & Rinaldo, Daniele, 2020. "Increasing risk: Dynamic mean-preserving spreads," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 69-82.
    8. Szölgyenyi Michaela, 2015. "Dividend maximization in a hidden Markov switching model," Statistics & Risk Modeling, De Gruyter, vol. 32(3-4), pages 143-158, December.
    9. Asmussen, Soren & Taksar, Michael, 1997. "Controlled diffusion models for optimal dividend pay-out," Insurance: Mathematics and Economics, Elsevier, vol. 20(1), pages 1-15, June.
    10. Christensen, Sören & Crocce, Fabián & Mordecki, Ernesto & Salminen, Paavo, 2019. "On optimal stopping of multidimensional diffusions," Stochastic Processes and their Applications, Elsevier, vol. 129(7), pages 2561-2581.
    11. Yang, Aijun & Liu, Yue & Xiang, Ju & Yang, Hongqiang, 2016. "Optimal buying at the global minimum in a regime switching model," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 50-55.
    12. Aleksandar Mijatovic & Martijn R. Pistorius, 2011. "On the drawdown of completely asymmetric Levy processes," Papers 1103.1460, arXiv.org, revised Sep 2012.
    13. Liu, Yue & Sun, Huaping & Meng, Bo & Jin, Shunlin & Chen, Bin, 2023. "How to purchase carbon emission right optimally for energy-consuming enterprises? Analysis based on optimal stopping model," Energy Economics, Elsevier, vol. 124(C).
    14. Michaela Szolgyenyi, 2016. "Dividend maximization in a hidden Markov switching model," Papers 1602.04656, arXiv.org.
    15. Lempa, Jukka & Mordecki, Ernesto & Salminen, Paavo, 2024. "Diffusion spiders: Green kernel, excessive functions and optimal stopping," Stochastic Processes and their Applications, Elsevier, vol. 167(C).
    16. Albert Cohen, 2018. "Editorial: A Celebration of the Ties That Bind Us: Connections between Actuarial Science and Mathematical Finance," Risks, MDPI, vol. 6(1), pages 1-3, January.

    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:eee:stapro:v:80:y:2010:i:11-12:p:950-957. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.