求解投資組合問題之全域最佳化方法

An Efficient Global Approach for Portfolio Optimization Problems

張志福(Chin-Fu Chang)

指導教授 ： 蔡榮發

國立臺北科技大學/管理學院/商業自動化與管理研究所/碩士(2011年)

https://doi.org/10.6841/NTUT.2011.00505

摘要

投資組合最佳化問題屬於二次整數規劃問題，所建構之問題可處理包含離散資產、交易費與邏輯限制式等。雖然有許多方法被提出來求解此問題，但僅能求得一區域最佳解或是可行解，並無法保證求出全域最佳解。故本研究運用一有效率的全域最佳化方法求解投資組合最佳化問題，把原先非線性模型轉換成線性模式，相較於目前之轉換方法，所提出之方法運用較少之二元變數與限制式，可有效降低模型的複雜度，增加計算上的效率。幾個投資組合範例也會被用來說明所提出方法之效用。

關鍵字

投資組合 ； 非線性整數規劃 ； 全域最佳解

並列摘要

Portfolio optimization problems are formulated as a quadratic integer program. The formulated model can handle discrete assets, transaction costs, and logical constraints. Although many optimization methods have been proposed to solve portfolio optimization problems, they usually can not guarantee to identify a global optimum but easily be trapped into a local optimum solution or a feasible solution. This study proposes an efficient global optimization method to find a global optimum of a portfolio optimization problem. A nonlinear portfolio selection model is transformed to a linear model with fewer binary variables and constraints. Comparing to the current methods, the proposed method can effectively improve the computational efficiency. Furthermore, this study utilizes some numerical examples to illustrate the effectiveness of the proposed method.

並列關鍵字

Portfolio selection ； Nonlinear integer programming ； Global optimization

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