| Summary: | 博士 === 國立交通大學 === 資訊管理所 === 87 === The research of portfolio optimization problems intends establishing mathematical models to decide the optimal capital allocation weights among assets. In 1952, Markowitz proposed the mean variance model to determine the optimization allocation weights of portfolios. However, there are scholars who believe the financial market to be efficient and then trying to outperform the market index is not a easy task. They proposed index portfolio models trying to determine the optimal investment weights to follow the index trend. The most popular index portfolio model is the estimated coefficient model proposed by Sharpe (1989).
No matter the mean variance model or the estimated coefficient model, they are both nonlinear mathematical programming models and cannot promise to obtain the global optimal solution. Furthermore, the nonlinear model is difficult to solve when considering more objective and subjective constraints in the original model.
In this thesis, two linear portfolio optimization models are proposed to improve the traditional models. And then, objective and subjective constraints are taken in consideration in the developed proposed models. The objective constraints considered in this research contain: (1) minimal investment unit limitation, (2) transaction cost consideration, and (3) limited investment category constraint. The subjective constraints come from more objectives other than original minimizing portfolio risk objective and maximizing portfolio return objective in the optimization process. After these objectives have been included in the proposed model, the programming models become multiple objective programming models, which are provided in this thesis as well.
Empirical tests in the Taiwan stock market are provided to verify that the proposed models are superior to the traditional models.
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