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Merging of opinions under uncertainty

Author

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  • Bier, Monika

    (Center for Mathematical Economics, Bielefeld University)

  • Engelage, Daniel

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We consider long-run behavior of agents assessing risk in terms of dynamic convex risk measures or, equivalently, utility in terms of dynamic variational preferences in an uncertain setting. By virtue of a robust representation, we show that all uncertainty is revealed in the limit and agents behave as expected utility maximizer under the true underlying distribution regardless of their initial risk anticipation. In particular, risk assessments of distinct agents converge. This result is a generalization of the fundamental Blackwell-Dubins Theorem, cp. [Blackwell & Dubins, 62], to convex risk. We furthermore show the result to hold in a non-time-consistent environment.

Suggested Citation

  • Bier, Monika & Engelage, Daniel, 2011. "Merging of opinions under uncertainty," Center for Mathematical Economics Working Papers 433, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:433
    as

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    References listed on IDEAS

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    1. Maccheroni, Fabio & Marinacci, Massimo & Rustichini, Aldo, 2006. "Dynamic variational preferences," Journal of Economic Theory, Elsevier, vol. 128(1), pages 4-44, May.
    2. Föllmer Hans & Penner Irina, 2006. "Convex risk measures and the dynamics of their penalty functions," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 1-36, July.
    3. Epstein, Larry G. & Marinacci, Massimo, 2007. "Mutual absolute continuity of multiple priors," Journal of Economic Theory, Elsevier, vol. 137(1), pages 716-720, November.
    4. Föllmer Hans & Penner Irina, 2006. "Convex risk measures and the dynamics of their penalty functions," Statistics & Risk Modeling, De Gruyter, vol. 24(1), pages 61-96, July.
    5. Riedel, Frank, 2004. "Dynamic coherent risk measures," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 185-200, August.
    6. 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.
    7. 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.
    8. Larry G. Epstein & Martin Schneider, 2007. "Learning Under Ambiguity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(4), pages 1275-1303.
    9. Frank Riedel, 2009. "Optimal Stopping With Multiple Priors," Econometrica, Econometric Society, vol. 77(3), pages 857-908, May.
    10. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    11. Alexander Schied, 2007. "Optimal investments for risk- and ambiguity-averse preferences: a duality approach," Finance and Stochastics, Springer, vol. 11(1), pages 107-129, January.
    12. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-577, May.
    13. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
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    Keywords

    Time consistency; Blackwell-Dubins; Multiple priors; Dynamic convex risk measures; Robust representation; Uncertainty;
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