Entropy and the value of information for investors

Pre-print, Working paper: 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.

Author(s)

Antonio Cabrales, Olivier Gossner, Roberto Serrano

Date of publication
  • 2011
Keywords JEL
C00 C43 D00 D80 D81 G00 G11
Keywords
  • Informativeness
  • Information structures
  • Entropy
  • Decision under uncertainty
  • Investment
  • Blackwell ordering
Internal reference
  • PSE Working Papers n°2011-40
Version
  • 1