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Entropy and the value of information for investors

Author

Listed:
  • Antonio Cabrales

    (Departamento de Economía - UC3M - Universidad Carlos III de Madrid [Madrid])

  • Olivier Gossner

    (PSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, LSE - London School of Economics and Political Science)

  • Roberto Serrano

    (Department of Economics - Brown University, Institute IMDEA Software [Madrid])

Abstract

Consider any investor who fears ruin when 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 is willing to buy $\beta$ at some price, he is also willing to buy $\alpha$ at that price. We show that this informativeness ordering is complete and is represented by the decrease in entropy of his beliefs, regardless of his preferences, initial wealth, or investment problem. We also show that no prior-independent informativeness ordering based on similar premises exists.

Suggested Citation

  • Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2011. "Entropy and the value of information for investors," PSE Working Papers halshs-00648884, HAL.
    • Handle: RePEc:hal:psewpa:halshs-00648884
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00648884
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    References listed on IDEAS

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    More about this item

    Keywords

    Informativeness; Information structures; Entropy; Decision under uncertainty; Investment; Blackwell ordering;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • D00 - Microeconomics - - General - - - General
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G00 - Financial Economics - - General - - - General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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