Entropy and the value of information for investors

Author Info

• 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 $\alpha$ is more informative than information structure $\beta$ if, whenever he is willing to buy $\beta$ at some price, he is also willing to buy $\alpha$ 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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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 661465000000000355.

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Handle: RePEc:cla:levarc:661465000000000355

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Find related papers by JEL classification:
• D14 - Microeconomics - - Household Behavior - - - Household Saving; Personal Finance
• D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
• D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
• G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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References

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1. Olivier Gossner & Penélope Hernández & Abraham Neyman, 2006. "Optimal Use of Communication Resources," Econometrica, Econometric Society, vol. 74(6), pages 1603-1636, November.
2. Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, vol. 58(1), pages 9-40, October.
3. Susan Athey & Jonathan Levin, 1998. "The Value of Information In Monotone Decision Problems," Working papers 98-24, Massachusetts Institute of Technology (MIT), Department of Economics.
4. Sergiu Hart, 2010. "Comparing Risks by Acceptance and Rejection," Discussion Paper Series dp531, The Center for the Study of Rationality, Hebrew University, Jerusalem.
5. 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.
6. Olivier Gossner, 2011. "Simple Bounds on the Value of a Reputation," Econometrica, Econometric Society, vol. 79(5), pages 1627-1641, 09.
7. Yaron Azrieli & Ehud Lehrer, 2004. "The Value Of A Stochastic Information Structure," Game Theory and Information 0411006, EconWPA.
8. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
9. Dean P. Foster & Sergiu Hart, 2009. "An Operational Measure of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 117(5), pages 785 - 814.
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Citations

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Cited by:
1. Camargo, Braz & Pastorino, Elena, 2012. "Career concerns: A human capital perspective," Textos para discussÃ£o 288, Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
2. Kyungmin Kim & Benjamin Lester & Braz Camargo, 2012. "Subsidizing Price Discovery," 2012 Meeting Papers 338, Society for Economic Dynamics.
3. Stark, Oded & Jakubek, Marcin & Falniowski, Fryderyk, 2013. "Reconciling the Rawlsian and the utilitarian approaches to the maximization of social welfare," University of Tuebingen Working Papers in Economics and Finance 65, University of Tuebingen, Faculty of Economics and Social Sciences.
4. Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2012. "The Appeal of Information Transactions," Economics Working Papers we1224, Universidad Carlos III, Departamento de Economía.
5. Stark, Oded & Jakubek, Marcin & Falniowski, Fryderyk, 2014. "Reconciling the Rawlsian and the utilitarian approaches to the maximization of social welfare," Discussion Papers 162881, University of Bonn, Center for Development Research (ZEF).

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