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Entropy and the Value of Information for Investors

38 Pages Posted: 8 Dec 2010  

Antonio Cabrales

Universidad Carlos III de Madrid

Olivier Gossner

Paris School of Economics (PSE)

Roberto Serrano

Brown University

Date Written: November 2010

Abstract

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.

Keywords: informativeness, information structures, entropy, decision under

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

Suggested Citation

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

Antonio Cabrales (Contact Author)

Universidad Carlos III de Madrid ( email )

CL. de Madrid 126
Madrid, Madrid 28903
Spain

Olivier Gossner

Paris School of Economics (PSE) ( email )

48 Boulevard Jourdan
Paris, 75014 75014
France

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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