This paper presents a continuous-time model of multiple-priors utility that allows for ambiguity aversion, distinguishing it from risk aversion and intertemporal substitution. The model extends stochastic differential utility by replacing a single prior with a set of priors, as in the atemporal model of Gilboa and Schmeidler. The resulting model, called recursive multiple-priors utility, provides a framework for analyzing asset returns in a representative agent setting. The model delivers restrictions on excess returns that admit interpretations reflecting a premium for risk and a separate premium for ambiguity. The paper shows that excess returns for a security can be expressed as a sum of a risk premium and an ambiguity premium. The model is applied to asset pricing, and it is shown that the model can help address two long-standing empirical puzzles: the equity premium puzzle and the home-bias puzzle. The paper also discusses the implications of ambiguity for asset markets, including the role of ambiguity in investment decisions and the potential for ambiguity to reduce the required degree of risk aversion. The paper also addresses the issue of learning in the presence of ambiguity, showing that ambiguity may persist even as an agent learns about her environment. The paper concludes by discussing the implications of the model for macroeconomic applications and the importance of focusing on behavior in understanding asset market dynamics.This paper presents a continuous-time model of multiple-priors utility that allows for ambiguity aversion, distinguishing it from risk aversion and intertemporal substitution. The model extends stochastic differential utility by replacing a single prior with a set of priors, as in the atemporal model of Gilboa and Schmeidler. The resulting model, called recursive multiple-priors utility, provides a framework for analyzing asset returns in a representative agent setting. The model delivers restrictions on excess returns that admit interpretations reflecting a premium for risk and a separate premium for ambiguity. The paper shows that excess returns for a security can be expressed as a sum of a risk premium and an ambiguity premium. The model is applied to asset pricing, and it is shown that the model can help address two long-standing empirical puzzles: the equity premium puzzle and the home-bias puzzle. The paper also discusses the implications of ambiguity for asset markets, including the role of ambiguity in investment decisions and the potential for ambiguity to reduce the required degree of risk aversion. The paper also addresses the issue of learning in the presence of ambiguity, showing that ambiguity may persist even as an agent learns about her environment. The paper concludes by discussing the implications of the model for macroeconomic applications and the importance of focusing on behavior in understanding asset market dynamics.