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Entropy and the value of information for investors

  • Serrano, Roberto
  • Gossner, Olivier
  • Cabrales, Antonio

Consider any investor who fears ruin facing any set of investments that satisfy noarbitrage. Before investing, he can purchase information about the state of nature in the form of an information structure. Given his prior, information structure α is more informative than information structure β if whenever he rejects α at some price, he also rejects β 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.

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Paper provided by Universidad Carlos III de Madrid. Departamento de Economía in its series UC3M Working papers. Economics with number we1104.

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Date of creation: Mar 2011
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Handle: RePEc:cte:werepe:we1104
Contact details of provider: Web page: http://www.eco.uc3m.es/

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  1. Jonathan Levin & Susan Athey, 2001. "The Value of Information in Monotone Decision Problems," Working Papers 01003, Stanford University, Department of Economics.
  2. Olivier Gossner & Abraham Neyman & Penélope Hernández, 2005. "Optimal Use Of Communication Resources," Working Papers. Serie AD 2005-06, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  3. Charles A. Holt & Susan K. Laury, 2002. "Risk Aversion and Incentive Effects," American Economic Review, American Economic Association, vol. 92(5), pages 1644-1655, December.
  4. Sergiu Hart, 2011. "Comparing Risks by Acceptance and Rejection," Journal of Political Economy, University of Chicago Press, vol. 119(4), pages 617 - 638.
  5. Dean Foster & Sergiu Hart, 2007. "An Operational Measure of Riskiness," Levine's Bibliography 843644000000000095, UCLA Department of Economics.
  6. Yaron Azrieli & Ehud Lehrer, 2004. "The Value Of A Stochastic Information Structure," Game Theory and Information 0411006, EconWPA.
  7. Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, vol. 58(1), pages 9-40, October.
  8. Olivier Gossner, 2011. "Simple Bounds on the Value of a Reputation," Econometrica, Econometric Society, vol. 79(5), pages 1627-1641, 09.
  9. Thierry Post & Martijn J. van den Assem & Guido Baltussen & Richard H. Thaler, 2008. "Deal or No Deal? Decision Making under Risk in a Large-Payoff Game Show," American Economic Review, American Economic Association, vol. 98(1), pages 38-71, March.
  10. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, June.
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