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Saint-Mont, Uwe

Comparing Different Information Levels

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  • Medientyp: E-Artikel
  • Titel: Comparing Different Information Levels
  • Beteiligte: Saint-Mont, Uwe
  • Erschienen: Bentham Science Publishers Ltd., 2017
  • Erschienen in: The Open Statistics & Probability Journal
  • Sprache: Englisch
  • DOI: 10.2174/1876527001708010007
  • ISSN: 1876-5270
  • Entstehung:
  • Anmerkungen:
  • Beschreibung: <jats:sec> <jats:title>Objective:</jats:title> <jats:p>Given a sequence of random variables X = <jats:italic>X<jats:sub>1</jats:sub></jats:italic>, <jats:italic>X<jats:sub>2</jats:sub></jats:italic>, . . .suppose the aim is to maximize one’s return by picking a ‘favorable’ <jats:italic>X<jats:sub>i</jats:sub></jats:italic>. Obviously, the expected payoff crucially depends on the information at hand. An optimally informed person knows all the values <jats:italic>X<jats:sub>i</jats:sub></jats:italic> = <jats:italic>x<jats:sub>i</jats:sub></jats:italic> and thus receives <jats:italic>E(sup X<jats:sub>i</jats:sub></jats:italic>).</jats:p> </jats:sec> <jats:sec> <jats:title>Method:</jats:title> <jats:p>We will compare this return to the expected payoffs of a number of gamblers having less information, in particular <jats:italic>sup<jats:sub>i</jats:sub>(EX<jats:sub>i</jats:sub>)</jats:italic>, the value of the sequence to a person who only knows the random variables’ expected values.</jats:p> <jats:p>In general, there is a stochastic environment, (F.E. a class of random variables <jats:italic>C</jats:italic>), and several levels of information. Given some <jats:bold>X</jats:bold>ϵ<jats:italic>C</jats:italic>, an observer possessing information <jats:italic>j</jats:italic> obtains <jats:italic>r<jats:sub>j</jats:sub></jats:italic>(<jats:bold>X</jats:bold>). We are going to study ‘information sets’ of the form.</jats:p> <jats:p>characterizing the advantage of <jats:italic>k</jats:italic> relative to <jats:italic>j</jats:italic>. 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.</jats:p> </jats:sec>
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