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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 (PSE)

Roberto Serrano

Brown University

November 2010

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 is more informative than information structure if whenever he rejects at some price, he also rejects 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.

Number of Pages in PDF File: 38

Keywords: informativeness, information structures, entropy, decision under

JEL Classification: C00, C43, D00, D80, D81, G00, G11

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Date posted: December 8, 2010  

Suggested Citation

Cabrales, Antonio and Gossner, Olivier and Serrano, Roberto, Entropy and the Value of Information for Investors (November 2010). Available at SSRN: http://ssrn.com/abstract=1720963 or http://dx.doi.org/10.2139/ssrn.1720963

Contact Information

Antonio Cabrales (Contact Author)
Universidad Carlos III de Madrid ( email )
CL. de Madrid 126
Madrid, Madrid 28903
Olivier Gossner
Paris School of Economics (PSE) ( email )
48 Boulevard Jourdan
Paris, 75014 75014
Roberto Serrano
Brown University ( email )
64 Waterman Street
Providence, RI 02912
United States
401-863-1036 (Phone)
401-863-1970 (Fax)
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