Entropy and the value of information for investors

Entropy and the value of information for investors — American Economic Review 103(1), 360–377 (2013)
Authors

Antonio Cabrales

Olivier Gossner

Roberto Serrano

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 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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American Economic Review 103(1), 360–377 (2013)

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Citation

BibTeX citation:
@article{cabrales2013,
  author = {Cabrales, Antonio and Gossner, Olivier and Serrano, Roberto},
  title = {Entropy and the Value of Information for Investors},
  journal = {American Economic Review},
  volume = {103},
  number = {1},
  pages = {360–377},
  date = {2013},
  url = {https://gossner.me/papers/entropy-and-the-value-of-information-to-investors.html},
  doi = {10.1257/aer.103.1.360},
  langid = {en},
  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 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.}
}
For attribution, please cite this work as:
Cabrales, Antonio, Olivier Gossner, and Roberto Serrano. 2013. “Entropy and the Value of Information for Investors.” American Economic Review 103 (1): 360–77. https://doi.org/10.1257/aer.103.1.360.