Entropy and the Value of Information for Investors

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. (JEL D14, D81, D83, G11)

[1]  Olivier Gossner,et al.  Simple Bounds on the Value of a Reputation , 2011 .

[2]  H. P. Binswanger.  Attitudes toward Risk: Theoretical Implications of an Experiment in Rural India , 1981 .

[3]  Tristan Tomala,et al.  Empirical Distributions of Beliefs Under Imperfect Observation , 2006, Math. Oper. Res..

[4]  D. Blackwell.  Equivalent Comparisons of Experiments , 1953 .

[5]  A. Rustichini,et al.  Ambiguity Aversion, Robustness, and the Variational Representation of Preferences , 2006 .

[6]  Lin Peng.  Learning with Information Capacity Constraints , 2005, Journal of Financial and Quantitative Analysis.

[7]  C. Sims.  Implications of rational inattention , 2003 .

[8]  Ehud Lehrer,et al.  The Value of a Stochastic Information Structure , 2008, Games Econ. Behav..

[9]  Penélope Hernández,et al.  Optimal use of communication resources , 2006 .

[10]  Sergiu Hart,et al.  Comparing Risks by Acceptance and Rejection , 2011, Journal of Political Economy.

[11]  N. Persico.  Information acquisition in auctions , 2000 .

[12]  Alvaro Sandroni.  Do markets favor agents able to make accurate predictions , 2000 .

[13]  R. Thaler,et al.  Deal or No Deal? Decision Making under Risk in a Large-Payoff Game Show , 2008 .

[14]  Sergiu Hart,et al.  An Operational Measure of Riskiness , 2009, Journal of Political Economy.

[15]  Robert J. Aumann,et al.  An Economic Index of Riskiness , 2008, Journal of Political Economy.

[16]  Juan José Ganuza,et al.  Signal Orderings Based on Dispersion and the Supply of Private Information in Auctions , 2010 .

[17]  L. Blume,et al.  Evolution and market behavior , 1992 .

[18]  Ehud Lehrer,et al.  The value of information - An axiomatic approach☆ , 1991 .

[19]  François Bourguignon,et al.  Decomposable Income Inequality Measures , 1979 .

[20]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.