IDEAS home Printed from https://ideas.repec.org/a/ben/tostpj/v8y2017i1p7-18.html
   My bibliography  Save this article

Comparing Different Information Levels

Author

Listed:
  • Uwe Saint-Mont

    (Nordhausen University of Applied Sciences, Nordhausen, Germany)

Abstract

Objective : Given a sequence of random variables X = X1, X2, . . .suppose the aim is to maximize one’s return by picking a ‘favorable’ Xi. Obviously, the expected payoff crucially depends on the information at hand. An optimally informed person knows all the values Xi = xi and thus receives E(sup Xi). Method : We will compare this return to the expected payoffs of a number of gamblers having less information, in particular supi(EXi), the value of the sequence to a person who only knows the random variables’ expected values. In general, there is a stochastic environment, (F.E. a class of random variables C), and several levels of information. Given some XϵC, an observer possessing information j obtains rj(X). We are going to study ‘information sets’ of the form. Rj,kC = {(x, y)|x = rj (X), y = rk(X), X ∈ C}, characterizing the advantage of k relative to j. Since such a set measures the additional payoff by virtue of increased information, its analysis yields a number of interesting results, in particular ‘prophet-type’ inequalities.

Suggested Citation

  • Uwe Saint-Mont, 2017. "Comparing Different Information Levels," The Open Statistics and Probability Journal, Bentham Open, vol. 8(1), pages 7-18, July.
    • Handle: RePEc:ben:tostpj:v:8:y:2017:i:1:p:7-18
    DOI: 10.2174/1876527001708010007
    as

    Download full text from publisher

    File URL: https://benthamopen.com/DOWNLOAD-PDF/TOSPJ-8-7/
    Download Restriction: no
    File URL: https://benthamopen.com/ABSTRACT/TOSPJ-8-7/
    Download Restriction: no
    File URL: https://libkey.io/10.2174/1876527001708010007?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
    ---><---

    References listed on IDEAS

    as
    1. Boshuizen, Frans, 1991. "Prophet region for independent random variables with a discount factor," Journal of Multivariate Analysis, Elsevier, vol. 37(1), pages 76-84, April.
    2. Kertz, Robert P., 1986. "Stop rule and supremum expectations of i.i.d. random variables: A complete comparison by conjugate duality," Journal of Multivariate Analysis, Elsevier, vol. 19(1), pages 88-112, June.
    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. Fabien Gensbittel & Dana Pizarro & Jérôme Renault, 2024. "Competition and Recall in Selection Problems," Dynamic Games and Applications, Springer, vol. 14(4), pages 806-845, September.
    2. Saint-Mont, Uwe, 2002. "A Simple Derivation of a Complicated Prophet Region," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 67-72, January.
    3. Sebastian Perez-Salazar & Victor Verdugo, 2024. "Optimal Guarantees for Online Selection Over Time," Papers 2408.11224, arXiv.org.

    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:ben:tostpj:v:8:y:2017:i:1:p:7-18. 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: Rehana Raza (email available below). General contact details of provider: .

    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.