The main objective of this thesis is to develop a smooth preferences structure under ambiguity that allows to represent an ambiguity averse behavior also in a context of continuous-time uncertainty. This is not achieved by prior smooth, ambiguity sensitive preferences models. The devised preferences structure is then used in two applications. First, I analyze the optimal portfolio choice, and its pricing consequences, for an ambiguity averse investor. It is shown that trading behaviors and pricing implications that are at odds with the traditional finance theory can be explained by ambiguity aversion. Second, I study the survival chances of ambiguity averse agents in a competitive economy. Under some conditions, smooth ambiguity averse agents can also survive when competing with the most rational agents, i.e. expected utility maximizers.