臺灣博碩士論文加值系統

如何將有限的資金在眾多之投資標的中作有效的配置，是財務管理領域中重
要的議題之一，稱為投資組合選擇，屬於一個多目標最佳化的問題。在過去大部分研究中，處理投資組合選擇問題大多是將具有衝突性的目標合併轉為單一目標的形式，並以單目標最佳化技術進行求解，但所得到的解未必是令人滿意的，因為並不能保證得到的解為非凌越解，特別當投資組合最佳化模型中包含一些實務上所需的限制條件，例如：基數限制，故本研究以啟發式多目標微粒群最佳化技術為基礎，運用背包型多目標微粒群最佳化演算法，針對投資組合問題進行求解，可在賣空和基數限制的條件下獲得效率之投資組合。其研究結果發現背包型多目標微粒群最佳化求得的非凌越解，在不被參考集凌越比例之績效衡量指標上顯示不易被LINGO求得之非凌越解所凌越。最後，針對投資組合選擇問題應用多屬性決策分析中的TOPSIS和簡單加權法兩種方法，對投資組合進行分析排序，提供投資者更多樣化之投資組合選擇，由研究結果可發現投資者在選擇其投資組合時，應考慮更多全面性的績效指標。

The allocation of limited capital to a variety of assets available is one of the important problems in financial management. It is actually a constrained multi-objective optimization problem called portfolio selection. Most studies have been made to solve the problem with single-objective optimization techniques by aggregating conflicting and incommensurate objectives into a single one. The solutions obtained may be unsatisfactory because their non-dominance is not guaranteed, especially when some practical constraints, such as cardinality constraints,
are incorporated into the portfolio optimization models. This paper presents an evolutionary multi-objective optimization technique, which called Knapsack
Multi-Objective Particle Swarm Optimization (K-MOPSO) to generate the efficient portfolios in terms of expected return and variance under short sales and/or cardinality
constraints. Computational results show that K-MOPSO is competitive with traditional approaches implemented by LINGO. Finally, a Multi-Attribute Decision Making (MADM) method named Technique for Order Preference by Similarity to
Ideal Solution (TOPSIS) is employed to outrank the efficient portfolio that decision makers satisfy most.

中文摘要…………………………………………………………… i
ABSTRACT ………………………………………………………… ii
誌 謝 …………………………………………………………… iii
目 錄 ……………………………………………………………………… iv
表目錄 ……………………………………………………………………… vii
圖目錄 ……………………………………………………………………… ix
第一章 緒論………………………………………………………………………1
1.1 研究背景與動機 ……………………………………………………………1
1.2 研究目的………………………………………………………………… 3
1.3 研究架構與流程…………………………………………………………… 3
1.4 研究限制 ………………………………………………………………… 4
第二章 文獻探討 ………………………………………………………………5
2.1 投資組合理論…………………………………………………………… 5
2.2 多目標最佳化 ……………………………………………………………12
2.2.1 柏拉圖最佳解集合………………………………………………………12
2.2.2 傳統多目標最佳化求解方式……………………………………………14
2.3.1 微粒群最佳化演算法的發展背景與基本概念…………………………16
2.3.2 微粒群演算法說明………………………………………………………17
2.3.3 微粒群演算法相關發展應用……………………………………………20
2.4 多屬性決策 ……………………………………………………………… 22
2.5.1 簡單加權法………………………………………………………………24
2.5.2 TOPSIS 方法……………………………………………………………26
第三章 多目標投資組合與微粒群最佳化………………………………………28
3.1 有偏好之投資組合模型……………………………………………………29
3.2 無偏好之多目標投資組合模型……………………………………………30
3.3 以LINGO軟體求解有偏好之投資組合模型………………………………32
3.3.1 LINGO軟體概述 ………………………………………………………32
3.3.2 LINGO模型的基本組成…………………………………………………33
3.4 K-MOPSO求解無偏好之多目標投資組合模型 ………………………… 34
3.4.1 K-MOPSO執行步驟 …………………………………………………35
3.4.2 K-MOPSO之系統建置…………………………………………………37
3.5 非凌越解績效評估……………………………………………………… 39
3.6 投資人偏好與投資組合………………………………………………… 40
3.6.1 簡單加權法……………………………………………………………40
3.6.2 TOPSIS法…………………………………………………………… 41
第四章 投資組合之實例驗證…………………………………………………42
4.1樣本資料……………………………………………………………………43
4.2 不允許賣空條件 …………………………………………………………45
4.2.1 無基數限制……………………………………………………………46
4.2.1.1 LINGO求解投資組合之結果……………………………………… 46
4.2.1.2 K-MOPSO求解投資組合之結果…………………………………… 52
4.2.1.3非凌越解績效評估………………………………………………… 55
4.2.2 基數限制………………………………………………………………61
4.2.2.1 LINGO求解投資組合之結果………………………………………61
4.2.2.2 K-MOPSO求解投資組合之結果……………………………………66
4.2.2.3非凌越解績效評估………………………………………………… 72
4.3 允許賣空條件……………………………………………………………81
4.3.1 無基數限制……………………………………………………………82
4.3.1.1 LINGO求解投資組合之結果………………………………………82
4.3.1.2 K-MOPSO求解投資組合之結果……………………………………83
4.3.1.3 非凌越解績效評估…………………………………………………85
4.3.2 基數限制………………………………………………………………88
4.3.2.1 LINGO求解投資組合之結果…………………………………… 88
4.3.2.2 K-MOPSO求解投資組合之結果……………………………………89
4.3.2.3 非凌越解績效評估…………………………………………………91
4.4 多屬性決策分析………………………………………………………97
4.4.1 簡單加權法求解投資組合……………………………………………98
4.4.2 TOPSIS求解投資組合………………………………………………100
第五章 研究結論與建議……………………………………………………106
5.1　研究結論 ……………………………………………………………106
5.2　未來研究建議……………………………………………………………108
參考文獻…………………………………………………………………………110
附 錄 一 ……………………………………………………………………115

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