A Continuous-Time Asset Pricing Model with Smooth Ambiguity Preferences

Abstract

This study extends the smooth ambiguity preferences model proposed by Klibanoff et al. (2005, 2009) to a continuous-time dynamic setting. It is known that these preferences converge to the subjective expected utility as the time interval shortens so that decision makers do not exhibit any ambiguity-sensitive behavior in the continuous-time limit. Accordingly, this study proposes an alternative model of decision making that applies Yaari’s (1987) dual theory to the original preferences and interchanges the role of the second-order utility function with that of the second-order probability. We then formulate a recursive utility of smooth ambiguity-sensitive decision makers in continuous-time. Our model is represented by the stochastic differential utility with distorted beliefs so that most existing techniques in financial studies can be made applicable together with these distorted beliefs. We give an asset-pricing example to demonstrate the applicability of our model.