A Smooth Model of Decision Making under Ambiguity
We propose and characterize a model of preferences over acts such that the decision maker prefers act f to act g if and only if E μ φ( E π u○f) ⩾ E μ φ( E π u○g), where E is the expectation operator, u is a von Neumann-Morgenstern utility function, φis an increasing transformation, and μis a subjective probability over the set Πof probability measures πthat the decision maker thinks are relevant given his subjective information. A key feature of our model is that it achieves a separation between ambiguity, identified as a characteristic of the decision maker's subjective beliefs, and ambiguity attitude, a characteristic of the decision maker's tastes. We show that attitudes toward pure risk are characterized by the shape of u, as usual, while attitudes toward ambiguity are characterized by the shape of φ. Ambiguity itself is defined behaviorally and is shown to be characterized by properties of the subjective set of measures Π. One advantage of this model is that the well-developed machinery for dealing with risk attitudes can be applied as well to ambiguity attitudes. The model is also distinct from many in the literature on ambiguity in that it allows smooth, rather than kinked, indifference curves. This leads to different behavior and improved tractability, while still sharing the main features (e.g., Ellsberg's paradox). The maxmin expected utility model (e.g., Gilboa and Schmeidler (1989)) with a given set of measures may be seen as a limiting case of our model with infinite ambiguity aversion. Two illustrative portfolio choice examples are offered. Copyright The Econometric Society 2005.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 73 (2005)
Issue (Month): 6 (November)
|Contact details of provider:|| Phone: 1 212 998 3820|
Fax: 1 212 995 4487
Web page: http://www.econometricsociety.org/
More information through EDIRC
|Order Information:|| Web: https://www.econometricsociety.org/publications/econometrica/access/ordering-back-issues Email: |
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Grant, S & Kajii, A & Polak, B, 1997.
"Temporal Resolution of Uncertainty and Recursive Non-Expected Utility Models,"
324, Australian National University - Department of Economics.
- Simon Grant & Atsushi Kajii & Ben Polak, 2000. "Temporal Resolution of Uncertainty and Recursive Non-Expected Utility Models," Econometrica, Econometric Society, vol. 68(2), pages 425-434, March.
- Sarin, Rakesh K & Wakker, Peter, 1992. "A Simple Axiomatization of Nonadditive Expected Utility," Econometrica, Econometric Society, vol. 60(6), pages 1255-72, November.
- Epstein, Larry G. & Miao, Jianjun, 2003.
"A two-person dynamic equilibrium under ambiguity,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 27(7), pages 1253-1288, May.
- Paolo Ghirardato & Massimo Marinacci, 2000.
"Risk, Ambiguity, and the Separation of Utility and Beliefs,"
Levine's Working Paper Archive
7616, David K. Levine.
- Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity and the Separation of Utility and Beliefs," Econometric Society World Congress 2000 Contributed Papers 1143, Econometric Society.
- Ghirardato, Paolo & Marinacci, Massimo, 2000. "Risk, Ambigity and the Separation of Utility and Beliefs," Working Papers 1085, California Institute of Technology, Division of the Humanities and Social Sciences.
- Massimo Marinacci & Paolo Ghirardato, 2001. "Risk, ambiguity, and the separation of utility and beliefs," ICER Working Papers - Applied Mathematics Series 21-2001, ICER - International Centre for Economic Research.
- Zengjing Chen & Larry G. Epstein, 2000.
"Ambiguity, risk and asset returns in continuous time,"
RCER Working Papers
474, University of Rochester - Center for Economic Research (RCER).
- Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
- Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
- Schmeidler, David, 1989.
"Subjective Probability and Expected Utility without Additivity,"
Econometric Society, vol. 57(3), pages 571-87, May.
- David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
- Uzi Segal, 1985.
"The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach,"
UCLA Economics Working Papers
362, UCLA Department of Economics.
- Segal, Uzi, 1987. "The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(1), pages 175-202, February.
- Kreps, David M & Porteus, Evan L, 1978.
"Temporal Resolution of Uncertainty and Dynamic Choice Theory,"
Econometric Society, vol. 46(1), pages 185-200, January.
- David M Kreps & Evan L Porteus, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Levine's Working Paper Archive 625018000000000009, David K. Levine.
- Loomes, Graham & Segal, Uzi, 1994.
"Observing Different Orders of Risk Aversion,"
Journal of Risk and Uncertainty,
Springer, vol. 9(3), pages 239-56, December.
- Itzhak Gilboa & David Schmeidler, 1989.
"Maxmin Expected Utility with Non-Unique Prior,"
- Segal, Uzi & Spivak, Avia, 1990.
"First order versus second order risk aversion,"
Journal of Economic Theory,
Elsevier, vol. 51(1), pages 111-125, June.
- Segal, Uzi, 1990.
"Two-Stage Lotteries without the Reduction Axiom,"
Econometric Society, vol. 58(2), pages 349-77, March.
- Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
- Larry G. Epstein & Jiankang Zhang, 1999.
"Subjective Probabilities on Subjectively Unambiguous Events,"
Carleton Economic Papers
99-18, Carleton University, Department of Economics.
- Epstein, Larry G & Zhang, Jiankang, 2001. "Subjective Probabilities on Subjectively Unambiguous Events," Econometrica, Econometric Society, vol. 69(2), pages 265-306, March.
When requesting a correction, please mention this item's handle: RePEc:ecm:emetrp:v:73:y:2005:i:6:p:1849-1892. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing)or (Christopher F. Baum)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.