Advertisement

Economic Theory

, Volume 67, Issue 1, pp 53–89 | Cite as

Ambiguity sensitive preferences in Ellsberg frameworks

  • Claudia RavanelliEmail author
  • Gregor Svindland
Research Article
  • 117 Downloads

Abstract

We study the market implications of ambiguity sensitive preferences using the \(\alpha \)-maxmin expected utility (\(\alpha \)-MEU) model. In the standard Ellsberg framework, we prove that \(\alpha \)-MEU preferences are equivalent to either maxmin, maxmax or subjective expected utility (SEU). We show how ambiguity aversion impacts equilibrium asset prices, and revisit the laboratory experimental findings in Bossaerts et al. (Rev Financ Stud 23:1325–1359, 2010). Only when there are three or more ambiguous states, \(\alpha \)-MEU, maxmin, maxmax and SEU models induce different portfolio choices. We suggest criteria to discriminate among these models in laboratory experiments and show that ambiguity seeking agents may prevent the existence of market equilibrium. Our results indicate that ambiguity matters for portfolio choice and does not wash out in equilibrium.

Keywords

Ellsberg framework \(\alpha \)-maxmin expected utility model Ambiguity aversion Portfolio choice Market equilibrium 

JEL Classification

G11 G12 C92 D53 

Notes

Acknowledgements

We are particularly indebted to Larry Epstein and Bill Zame for insightful discussions. For helpful comments we thank Peter Bossaerts, Pierre Collin-Dufresne, Darrell Duffie, Damir Filipovic, Lorenzo Garlappi, Paolo Ghirardato, Julien Hugonnier, Pablo Koch-Medina, Leonid Kogan, Loriano Mancini and Jean-Charles Rochet, as well as the participants of the 2016 Risk and Stochastics Conference at London School of Economics.

References

  1. Ahn, D., Choi, S., Gale, D., Kariv, S.: Estimating ambiguity aversion in a portfolio choice experiment. Quant. Econ. 5(2), 195–223 (2014)CrossRefGoogle Scholar
  2. Arrow, K., Hurwicz, L.: An optimality criterion for decision making under ignorance. In: Carter, C.F., Ford, J.L. (eds.) Uncertainty and Expectations in Economics. Basil Blackwell, Oxford (1972)Google Scholar
  3. Bossaerts, P., Ghirardato, P., Guarnaschelli, S., Zame, W.: Ambiguity in asset markets: theory and experiments. Rev. Financ. Stud. 23, 1325–1359 (2010)CrossRefGoogle Scholar
  4. Boyle, P., Garlappi, L., Uppal, R., Wang, T.: Keynes meets Markowitz: the trade-off between familiarity and diversification. Manag. Sci. 58, 253–272 (2012)CrossRefGoogle Scholar
  5. Cao, H.H., Wang, T., Zhang, H.: Model uncertainty, limited market participation, and asset prices. Rev. Financ. Stud. 18, 1219–1251 (2005)CrossRefGoogle Scholar
  6. Cao, H.H., Han, B., Hirshleifer, D., Zhang, H.H.: Fear of the unknown: familiarity and economic decisions. Rev. Finance 15, 173–206 (2011)CrossRefGoogle Scholar
  7. Chen, Y., Katuščák, P., Ozdenoren, E.: Sealed bid auctions with ambiguity: theory and experiments. J. Econ. Theory 136, 513–535 (2007)CrossRefGoogle Scholar
  8. Chen, Z., Epstein, L.: Ambiguity, risk, and asset returns in continuous time. Econometrica 70, 1403–1443 (2002)CrossRefGoogle Scholar
  9. Cubitt, R., van de Kuilen, G., Mukerji, S.: Discriminating Between Models of Ambiguity Attitude: A Qualitative Test. Mimeo, University of Oxford, Oxford (2014)Google Scholar
  10. De Castro, L., Yannelis, N.C.: Uncertainty, efficiency and incentive compatibility, Working Paper (2016)Google Scholar
  11. De Castro, L., Pesce, M., Yannelis, N.C.: Rational expectations equilibrium under ambiguity. Working Paper (2017)Google Scholar
  12. Dimmock, S.G., Kouwenberg, R., Wakker, P.P.: Ambiguity attitudes in a large representative sample. Manag. Sci. 62, 1363–1380 (2016)CrossRefGoogle Scholar
  13. Dow, J., Werlang, S.R.D.C.: Uncertainty aversion, risk aversion, and the optimal choice of portfolio. Econometrica 60, 197–204 (1992)CrossRefGoogle Scholar
  14. Easley, D., O’Hara, M.: Ambiguity and nonparticipation: the role of regulation. Rev. Financ. Stud. 22(5), 1817–1843 (2009)CrossRefGoogle Scholar
  15. Eichberger, J., Grant, S., Kelsey, D., Koshevoy, G.A.: The \(\alpha \)-MEU model: a comment. J. Econ. Theory 146, 1684–1698 (2011)CrossRefGoogle Scholar
  16. Ellsberg, D.: Risk, ambiguity, and the savage axioms. Q. J. Econ. 75, 643–669 (1961)CrossRefGoogle Scholar
  17. Epstein, L., Schneider, M.: Ambiguity, information quality, and asset pricing. J. Finance 63, 197–228 (2008)CrossRefGoogle Scholar
  18. Epstein, L., Schneider, M.: Ambiguity and asset markets. Annu. Rev. Financ. Econ. 2, 315–346 (2010)CrossRefGoogle Scholar
  19. Epstein, L.G., Miao, J.: A two-person dynamic equilibrium under ambiguity. J. Econ. Dyn. Control 27, 1253–1288 (2003)CrossRefGoogle Scholar
  20. Ghirardato, P., Klibanoff, P., Marinacci, M.: Additivity with multiple priors. J. Math. Econ. 30, 405–420 (1998)CrossRefGoogle Scholar
  21. Ghirardato, P., Maccheroni, F., Marinacci, M.: Differentiating ambiguity and ambiguity attitude. J. Econ. Theory 118, 133–173 (2004)CrossRefGoogle Scholar
  22. Gilboa, I., Marinacci, M.: Ambiguity and the Bayesian paradigm. In: Acemoglu, D., Arellano, M., Dekel, E. (eds.) Advances in Economics and Econometrics: Theory and Applications, Tenth World Congress of the Econometric Society. Cambridge University Press, New York (2013)Google Scholar
  23. Gilboa, I., Schmeidler, D.: Maxmin expected utility with non-unique prior. J. Math. Econ. 18, 141–153 (1989)CrossRefGoogle Scholar
  24. He, W., Yannelis, N.C.: Equilibrium theory under ambiguity. J. Math. Econ. 61, 86–95 (2015)CrossRefGoogle Scholar
  25. Hurwicz, L.: Optimality criteria for decision making under ignorance. Discussion Paper 370, Cowles Commission (1951a)Google Scholar
  26. Hurwicz, L.: Some specification problems and application to econometric models. Econometrica 19, 343–344 (1951b)Google Scholar
  27. Illeditsch, P.: Ambiguous information, portfolio inertia, and excess volatility. J. Finance 66, 2213–2247 (2011)CrossRefGoogle Scholar
  28. Jaffray, J.Y.: Application of linear utility theory to belief functions. In: Bouchon, B., Saitta, L., Yager, R.R. (eds.) Uncertainty and Intelligent Systems. IPMU 1988. Lecture Notes in Computer Science, vol. 313, pp. 1–8. Springer, Berlin, Heidelberg (1988)Google Scholar
  29. Klibanoff, P., Mukerji, S., Seo, K.: Perceived ambiguity and relevant measures. Econometrica 82, 1945–1978 (2014)CrossRefGoogle Scholar
  30. Knight, F.: Risk, Uncertainty and Profit. Houghton, Mifflin, Boston (1921)Google Scholar
  31. Machina, M.J., Siniscalchi, M.: Ambiguity and ambiguity aversion. In: Machina, M.J., Viscusi, W.K. (eds.) Handbook of the Economics of Uncertainty. Elsevier, Amsterdam (2014)Google Scholar
  32. Marinacci, M.: Probabilistic sophistication and multiple priors. Econometrica 70, 755–764 (2002)CrossRefGoogle Scholar
  33. Olszewski, W.: Preferences over sets of lotteries. Rev. Econ. Stud. 74, 567–595 (2007)CrossRefGoogle Scholar
  34. Rockafellar, R.T.: Convex analysis. Princeton mathematical series, Princeton University Press (1970)Google Scholar
  35. Siniscalchi, M.: A behavioral characterization of plausible priors. J. Econ. Theory 128, 91–135 (2006)CrossRefGoogle Scholar
  36. Trojani, F., Vanini, P.: Robustness and ambiguity aversion in general equilibrium. Rev. Finance 8, 279–324 (2004)CrossRefGoogle Scholar
  37. Uppal, R., Wang, T.: Model misspecification and underdiversification. J. Finance 58, 2465–2486 (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Banking and Finance, Center for Finance and InsuranceUniversity of ZurichZurichSwitzerland
  2. 2.Mathematics InstituteLMU MunichMunichGermany

Personalised recommendations