Optimal Stopping under Ambiguity
We consider optimal stopping problems for ambiguity averse decision makers with multiple priors. In general, backward induction fails. If, however, the class of priors is time-consistent, we establish a generalization of the classical theory of optimal stopping. To this end, we develop first steps of a martingale theory for multiple priors. We define minimax (super)martingales, provide a Doob-Meyer decomposition, and characterize minimax martingales. This allows us to extend the standard backward induction procedure to ambiguous, time-consistent preferences. The value function is the smallest process that is a minimax supermartingale and dominates the payoff process. It is optimal to stop when the current payoff is equal to the value function. Moving on, we study the infinite horizon case. We show that the value process satisfies the same backward recursion (Bellman equation) as in the finite horizon case. The finite horizon solutions converge to the infinite horizon solution. Finally, we characterize completely the set of time-consistent multiple priors in the binomial tree. We solve two classes of examples: the so-called independent and indistinguishable case (the parking problem) and the case of American Options (Cox-Ross-Rubinstein model).
|Date of creation:||14 Dec 2010|
|Date of revision:|
|Contact details of provider:|| Postal: Postfach 10 01 31, 33501 Bielefeld|
Web page: http://www.imw.uni-bielefeld.de/
More information through EDIRC
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.:
- Massimo Marinacci & Fabio Maccheroni & Alain Chateauneuf & Jean-Marc Tallon, 2003.
"Monotone Continuous Multiple Priors,"
ICER Working Papers - Applied Mathematics Series
30-2003, ICER - International Centre for Economic Research.
- Alain Chateauneuf & Fabio Macheronni & Massimo Marinacci & Jean-Marc Tallon, 2005. "Monotone continuous multiple priors," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00177057, HAL.
- Eichberger, Jurgen & Kelsey, David, 1996.
"Uncertainty Aversion and Dynamic Consistency,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(3), pages 625-40, August.
- Itzhak Gilboa & David Schmeidler, 1989.
"Maxmin Expected Utility with Non-Unique Prior,"
- Larry G. Epstein & Martin Schneider, 2001.
RCER Working Papers
485, University of Rochester - Center for Economic Research (RCER).
- Föllmer, Hans & Kabanov, Jurij M., 1997.
"Optional decomposition and lagrange multipliers,"
SFB 373 Discussion Papers
1997,54, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Riedel, Frank, 2004.
"Dynamic coherent risk measures,"
Stochastic Processes and their Applications,
Elsevier, vol. 112(2), pages 185-200, August.
When requesting a correction, please mention this item's handle: RePEc:bie:wpaper:390. 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: (Bettina Weingarten)
If references are entirely missing, you can add them using this form.