Portfolio optimization in an uncertain environment has great practical value in investment decision process. But this area is highly fragmented due to fast evolution of market structure and changing investor behavior. In this dissertation, four methods are investigated/designed to explore their efficiency under different circumstances. Parametric portfolio decomposes weights by set of factors whose coefficients are uniquely determined via maximizing utility function. A robust bootstrap method is proposed to assist factor selection. If investors exhibit asymmetric aversion of tail risk, pessimistic models on Choquet utility maximization and coherent risk measures acquire superiority. A new hybrid method that inherits advantage of parameterization and tail risk minimization is designed. Mean-variance, which is optimal with elliptical return distribution, should be employed in the case of capital allocation to trading strategies. Nonparametric classifiers may enhance homogeneity of inputs before feeding the optimizer. Traditional factor portfolio can be extended to functional settings by applying FPCA to return curves sorted by factors. Diversification is always achieved by mixing with detected nonlinear components. This research contributes to existing literature on portfolio choice in three-folds: strength and weakness of each method is clarified; new models that outperform traditional approaches are developed; empirical studies are used to facilitate comparison.
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