We introduce and axiomatize dynamic variational preferences, the dynamic version of the variational preferences we axiomatized in [F. Maccheroni, M. Marinacci, A. Rustichini, Ambiguity aversion, robustness, and the variational representation of preferences, Mimeo, 2004], which generalize the multiple priors preferences of Gilboa and Schmeidler [Maxmin expected utility with a non-unique prior, J. Math. Econ. 18 (1989) 141-153], and include the Multiplier Preferences inspired by robust control and first used in macroeconomics by Hansen and Sargent (see [L.P. Hansen, T.J. Sargent, Robust control and model uncertainty, Amer. Econ. Rev. 91 (2001) 60-66]), as well as the classic Mean Variance Preferences of Markovitz and Tobin. We provide a condition that makes dynamic variational preferences time consistent, and their representation recursive. This gives them the analytical tractability needed in macroeconomic and financial applications. A corollary of our results is that Multiplier Preferences are time consistent, but Mean Variance Preferences are not.
Bibliographical noteFunding Information:
We thank Erio Castagnoli, Larry Epstein, Gino Favero, Salvatore Modica, Sergio Segre, Claudio Tebaldi, several seminar audiences, and, especially, Thomas Sargent and three anonymous referees for some very helpful comments. Part of this research was done while the first two authors were visiting in Spring 2004 the Department of Economics of Boston University and CERMSEM (Université Paris 1), which they thank for their hospitality. They also gratefully acknowledge the financial support of the Ministero dell’Istruzione, dell’Università e della Ricerca. Rustichini gratefully acknowledges the financial support of the National Science Foundation (Grant # 0136556).
- Ambiguity aversion
- Model uncertainty
- Recursive utility
- Rubust control
- Time consistency