混合投資組合問題之近似全域最佳解法

Abstract

本研究改善Markowitz投資組合模式，提出一混合投資組合模式，主要的 優點有：1.能同時對兩類不同投資性質的投資項目進行投資組合選取，其 中連續變數投資項目（例如：股票）可投資任意金額、整數變數投資項目 （例如：房地產）只有選擇投資和不選擇投資兩種可能；2.本模式能求得 近似全域最佳解。本研究所提出之模式為一非線性的混合零壹多項式規劃 問題，為解決此一問題，本文發展一線性轉換法，能將問題轉換為一個近 似的混合零壹線性規劃問題，並在目標式之最大容許誤差可預先設定的情 況下，控制求解時間，且求得混合投資組合問題之近似全域最佳解法。 This paper proposes a new portfolio model of investment, which is a modification of Markowitz's model.The advantages of this proposed model are : 1)it can deal with investment projects containing both the continuous items(such as stocks) and the discrete items(such as real estates); 2)it can find the solution which is as close as possible to the global optimum.We first formulate a portfolio problem as a nonlinear mixed integer program.After that,we develop a linearization technique to transform the formulated program into a linear mixed integer program.The user can specify the tolerant level of the solution in order to find an approximately global optimum at reasonable computational time.