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Crisp monetary acts in multiple-priors models of decision under ambiguity

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  • André, Eric

Abstract

In axiomatic models of decision under ambiguity using a set of priors, a clear distinction can be made between acts which are affected by ambiguity and those which are not: the crisp acts. In these multiple-priors models, the decision maker is indifferent between holding a constant act or holding a non constant crisp act with the same expected utility, if it exists. In financial settings, we show that this indifference, together with the standard definition of monetary acts in the Anscombe–Aumann framework, implies that the investor ignores the variance of some assets, a behavior which conflicts with the assumption on which modern portfolio theory has been built. In this paper we establish the geometrical and topological properties of the set of priors that rule out the existence of non constant crisp acts. These properties in turn restrict what can possibly be an unambiguous financial asset.

Suggested Citation

  • André, Eric, 2016. "Crisp monetary acts in multiple-priors models of decision under ambiguity," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 153-161.
  • Handle: RePEc:eee:mateco:v:67:y:2016:i:c:p:153-161
    DOI: 10.1016/j.jmateco.2016.10.001
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    1. Tomasz Strzalecki, 2011. "Axiomatic Foundations of Multiplier Preferences," Econometrica, Econometric Society, vol. 79(1), pages 47-73, January.
    2. Fabio Maccheroni & Massimo Marinacci & Doriana Ruffino, 2013. "Alpha as Ambiguity: Robust Mean‐Variance Portfolio Analysis," Econometrica, Econometric Society, vol. 81(3), pages 1075-1113, May.
    3. Massimo Guidolin & Francesca Rinaldi, 2013. "Ambiguity in asset pricing and portfolio choice: a review of the literature," Theory and Decision, Springer, vol. 74(2), pages 183-217, February.
    4. Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M. & Montrucchio, L., 2011. "Uncertainty averse preferences," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1275-1330, July.
    5. Phelim Boyle & Lorenzo Garlappi & Raman Uppal & Tan Wang, 2012. "Keynes Meets Markowitz: The Trade-Off Between Familiarity and Diversification," Management Science, INFORMS, vol. 58(2), pages 253-272, February.
    6. Chateauneuf, Alain & Faro, José Heleno, 2009. "Ambiguity through confidence functions," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 535-558, September.
    7. Nehring, Klaus, 1999. "Capacities and probabilistic beliefs: a precarious coexistence," Mathematical Social Sciences, Elsevier, vol. 38(2), pages 197-213, September.
    8. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    9. Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2010. "Objective and Subjective Rationality in a Multiple Prior Model," Econometrica, Econometric Society, vol. 78(2), pages 755-770, March.
    10. Paolo Ghirardato & Marciano Siniscalchi, 2012. "Ambiguity in the Small and in the Large," Econometrica, Econometric Society, vol. 80(6), pages 2827-2847, November.
    11. Alain Chateauneuf & Fabio Maccheroni & Massimo Marinacci & Jean-Marc Tallon, 2005. "Monotone continuous multiple priors," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 973-982, November.
    12. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    13. Epstein, Larry G & Zhang, Jiankang, 2001. "Subjective Probabilities on Subjectively Unambiguous Events," Econometrica, Econometric Society, vol. 69(2), pages 265-306, March.
    14. ,, 2016. "Objective rationality and uncertainty averse preferences," Theoretical Economics, Econometric Society, vol. 11(2), May.
    15. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    16. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    17. Marciano Siniscalchi, 2009. "Vector Expected Utility and Attitudes Toward Variation," Econometrica, Econometric Society, vol. 77(3), pages 801-855, May.
    18. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2003. "A Subjective Spin on Roulette Wheels," Econometrica, Econometric Society, vol. 71(6), pages 1897-1908, November.
    19. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    20. Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2011. "Rational preferences under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 341-375, October.
    21. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    22. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    23. Jiankang Zhang, 2002. "Subjective ambiguity, expected utility and Choquet expected utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 159-181.
    24. Larry G. Epstein, 1999. "A Definition of Uncertainty Aversion," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(3), pages 579-608.
    25. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, June.
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