IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1911.11971.html
   My bibliography  Save this paper

With or without replacement? Sampling uncertainty in Shepp's urn scheme

Author

Listed:
  • Kristoffer Glover

Abstract

We introduce a variant of Shepp's classical urn problem in which the optimal stopper does not know whether sampling from the urn is done with or without replacement. By considering the problem's continuous-time analog, we provide bounds on the value function and in the case of a balanced urn (with an equal number of each ball type) an explicit solution is found. Surprisingly, the optimal strategy for the balanced urn is the same as in the classical urn problem.

Suggested Citation

  • Kristoffer Glover, 2019. "With or without replacement? Sampling uncertainty in Shepp's urn scheme," Papers 1911.11971, arXiv.org, revised Mar 2022.
    • Handle: RePEc:arx:papers:1911.11971
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1911.11971
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jun Liu, 2004. "Losing Money on Arbitrage: Optimal Dynamic Portfolio Choice in Markets with Arbitrage Opportunities," The Review of Financial Studies, Society for Financial Studies, vol. 17(3), pages 611-641.
    2. Marco Avellaneda & Michael Lipkin, 2003. "A market-induced mechanism for stock pinning," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 417-425.
    3. Brennan, Michael J & Schwartz, Eduardo S, 1990. "Arbitrage in Stock Index Futures," The Journal of Business, University of Chicago Press, vol. 63(1), pages 7-31, January.
    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. Bernardo D’Auria & Alessandro Ferriero, 2020. "A Class of Itô Diffusions with Known Terminal Value and Specified Optimal Barrier," Mathematics, MDPI, vol. 8(1), pages 1-14, January.
    2. Glover, Kristoffer, 2022. "Optimally stopping a Brownian bridge with an unknown pinning time: A Bayesian approach," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 919-937.
    3. Abel Azze & Bernardo D'Auria & Eduardo Garc'ia-Portugu'es, 2022. "Optimal stopping of Gauss-Markov bridges," Papers 2211.05835, arXiv.org, revised Dec 2023.
    4. Bahman Angoshtari & Tim Leung, 2019. "Optimal dynamic basis trading," Annals of Finance, Springer, vol. 15(3), pages 307-335, September.
    5. Bahman Angoshtari & Tim Leung, 2020. "Optimal trading of a basket of futures contracts," Annals of Finance, Springer, vol. 16(2), pages 253-280, June.
    6. Basak, Suleyman & Croitoru, Benjamin, 2006. "On the role of arbitrageurs in rational markets," Journal of Financial Economics, Elsevier, vol. 81(1), pages 143-173, July.
    7. Görgens, Maik & Thulin, Måns, 2014. "Bias-correction of the maximum likelihood estimator for the α-Brownian bridge," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 78-86.
    8. Xiaodong Chen & Tim Leung & Yang Zhou, 2022. "Constrained dynamic futures portfolios with stochastic basis," Annals of Finance, Springer, vol. 18(1), pages 1-33, March.
    9. Jun Liu, 2004. "Losing Money on Arbitrage: Optimal Dynamic Portfolio Choice in Markets with Arbitrage Opportunities," The Review of Financial Studies, Society for Financial Studies, vol. 17(3), pages 611-641.
    10. Adrian, Tobias, 2009. "Inference, arbitrage, and asset price volatility," Journal of Financial Intermediation, Elsevier, vol. 18(1), pages 49-64, January.
    11. Adrian, Tobias & Borowiecki, Karol Jan & Tepper, Alexander, 2022. "A leverage-based measure of financial stability," Journal of Financial Intermediation, Elsevier, vol. 51(C).
    12. Eckhard Platen, 2008. "A Unifying Approach to Asset Pricing," Research Paper Series 227, Quantitative Finance Research Centre, University of Technology, Sydney.
    13. Tan, Senren & Jin, Zhuo & Wu, Fuke, 2015. "Arbitrage and leverage strategies in bubbles under synchronization risks and noise-trader risks," Economic Modelling, Elsevier, vol. 49(C), pages 331-343.
    14. Ahoniemi, Katja & Lanne, Markku, 2009. "Joint modeling of call and put implied volatility," International Journal of Forecasting, Elsevier, vol. 25(2), pages 239-258.
    15. repec:cty:dpaper:10.1080/14697680701881763 is not listed on IDEAS
    16. Urcola, Hernan A. & Irwin, Scott H., 2006. "Has the Performance of the Hog Options Market Changed?," 2006 Annual meeting, July 23-26, Long Beach, CA 21479, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    17. Yi‐Wei Chuang & Wei‐Che Tsai & Ming‐Hung Wu, 2020. "The impact of net buying pressure on VIX option prices," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(2), pages 209-227, February.
    18. Sercu, Piet & Vandebroek, Martina, 2005. "What UIP tests on extreme samples reveal about the missing variable," Journal of International Money and Finance, Elsevier, vol. 24(8), pages 1237-1260, December.
    19. Jiao Li, 2016. "Trading VIX Futures under Mean Reversion with Regime Switching," Papers 1605.07945, arXiv.org, revised Jun 2016.
    20. Dwyer, Gerald P, Jr & Locke, Peter R & Yu, Wei, 1996. "Index Arbitrage and Nonlinear Dynamics between the S&P 500 Futures and Cash," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 301-332.
    21. Kristoffer Glover & Hardy Hulley, 2022. "Financially constrained index futures arbitrage," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(9), pages 1688-1703, September.

    More about this item

    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:1911.11971. 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.