Dynamic portfolio optimization using mean-semivariance
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This dissertation studies the mean-semivariance portfolio optimization problem. We describe the relationship of this kind of optimization in the context of other types of portfolio optimization. We construct a novel analysis of mean-semivariance in the context of piecewise quadratic optimization. The unique structure of mean-semivariance is leveraged to provide insight into properties of the optimal portfolio as a function of its key input parameters. This characterization allows us to introduce a new approach to solving a multi-period dynamic mean-semivariance portfolio problem. The proposed methodology provides significant improvements over naive approaches not leveraging the unique structure of the mean-semivariance value function. Finally, we develop a novel, distributionally robust piecewise quadratic formulation using semidefinite programming. We apply the robust formulation to the mean-semivariance portfolio problem to construct a distributionally robust mean-semivariance portfolio. We prove that the robust mean-semivariance portfolio is actually equivalent to the classical mean-variance portfolio.