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Comparing Different Information Levels

Author

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  • 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
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    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.
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    1. Saint-Mont, Uwe, 2002. "A Simple Derivation of a Complicated Prophet Region," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 67-72, January.

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