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Entropy and the value of information for investors

  • Antonio Cabrales

    ()

    (Universidad Carlos III de Madrid)

  • Olivier Gossner

    ()

    (Paris School of Economics and LSE)

  • Roberto Serrano

    ()

    (Brown University and IMDEA Social Sciences Institute)

Consider any investor who fears ruin facing any set of investments that satisfy no-arbitrage. Before investing, he can purchase information about the state of nature in the form of an information structure. Given his prior, information structure alpha is more informative than information structure beta if whenever he rejects alpha at some price, he also rejects beta at that price. We show that this complete informativeness ordering is represented by the decrease in entropy of his beliefs, regardless of his preferences, initial wealth or investment problem. It is also shown that no prior-independent informativeness ordering based on similar premises exists.

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Paper provided by Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales in its series Working Papers with number 2010-23.

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Date of creation: 06 Dec 2010
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Publication status: Forthcoming in American Economic Review
Handle: RePEc:imd:wpaper:wp2010-23
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