This dissertation focuses on testing and identifying individual ambiguity preference under the framework of "smooth ambiguity preference" developed by Klibanoff, Marinacci, and Mukerji (2005). Following the seminal contributions of Allais (1953) and Ellsberg (1961), experimental data have consistently demonstrated that individuals do not behave in accordance with predictions of the expected utility model when they face uncertainty. As one important class of ambiguity utility, the smooth ambiguity model distinguishes ambiguity aversion from risk aversion, which makes the comparative statics possible. However, currently there is little work on testing and recovering such preferences based on observable choices. The dissertation contains four parts. Chapter 2 uses two approaches to derive the necessary and sufficient conditions for observed individual portfolio choice to be compatible with the smooth ambiguity preference. The first approach is the revealed preference method, and is based on finite observations. The second approach is demand function testing, and is based on infinite observations. Chapter 3 establishes the conditions under which the smooth ambiguity preference can be uniquely identified from individual demand functions. In Chapter 4, I extend the argument of Varian (1988) to multiple observations and incomplete market case to non-parametrically test different shapes of risk aversion, and then to test hypotheses on shapes of ambiguity aversion. In Chapter 5, to use household survey data to identify household risk and ambiguity aversion, I build a simple parametric model to identify household risk and ambiguity aversion from their saving and portfolio choice. The data from the Bank of Italy Survey on Household Income and Wealth 2008 and 2010 support the constant relative risk aversion and constant relative ambiguity aversion hypothesis, and give evidence of the magnitude of household risk and ambiguity aversion.