Comparing Different Information Levels

Uwe Saint-Mont ()
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Uwe Saint-Mont: Nordhausen University of Applied Sciences, Nordhausen, Germany

The Open Statistics and Probability Journal, 2017, vol. 8, issue 1, 7-18

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.

Keywords: Stochastic comparisons; Information levels; Prophet regions; Inverse functions. (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:ben:tostpj:v:8:y:2017:i:1:p:7-18

DOI: 10.2174/1876527001708010007

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