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Entropy and the value of information for investors

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  • Antonio Cabrales
  • Olivier Gossner
  • Roberto Serrano

Abstract

Consider an investor who fears ruin when facing investments that satisfy no-arbitrage. Before investing he can purchase information about the state of nature as an information structure. Given his prior, information structure α investment dominates information structure β if, whenever he is willing to buy β at some price, he is also willing to buy α 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.
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Suggested Citation

  • Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2010. "Entropy and the value of information for investors," Levine's Working Paper Archive 661465000000000355, David K. Levine.
    • Handle: RePEc:cla:levarc:661465000000000355
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    More about this item

    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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