臺灣博碩士論文加值系統

由於現今全球經濟成長趨緩，微薄的薪資與定期存款之利息無法因應通貨膨脹所造成的影響，因此投資理財已成為大眾關注之重要焦點。人工蜂群演算法（Artificial Bee Colony；ABC）為近年來於最佳化領域中受到關注的萬用啟發式演算法之一，其為模擬自然界中蜜蜂覓食行為之原理所發展的一種群體智慧演算法（Swarm Intelligence）。因此，本研究使用人工蜂群演算法求解投資組合最佳化問題（Portfolio Optimization Problem），為投資者提供有效之投資組合，作為投資參考之依據。本研究以Markowitz之平均數-變異數模型（Mean-Variance Portfolio Model；M-V模型）為基礎，針對不同屬性之投資者分別考慮下方標準差（Downside Standard Deviation；DSD）與上方標準差（Upside Standard Deviation；USD）適當修正投資組合模型，以人工蜂群演算法以不同資料期間及不同規模大小之例題求解各不同模型，並與變動鄰域搜尋法（Variable Neighborhood Search；VNS）、模擬退火演算法（Simulated Annealing；SA）及禁忌搜尋演算法（Tabu Search；TS）進行比較。結果顯示人工蜂群演算法具有較佳之績效，尤其以考慮柏拉圖選取策略之ABC II表現最佳，也成功驗證本研究提出之人工蜂群演算法適用於求解投資組合最佳化問題，並提供不同屬性之投資者作為投資參考之依據。

As global economy of today is slowdown and meager salary and interest of term deposit can’t adjust to the impact of inflation, financial investment has become an important focus of public concern. Artificial Bee Colony (ABC), one of metaheuristic algorithms, has attracted lots of attention in optimization field in recent years. ABC, employing the idea of swarm intelligence, simulates the principle of bee foraging behavior in the nature. Thus, this study adopts ABC to solve Portfolio Optimization Problem, and to provide effective portfolio as a reference basis of investment for investors. This study, based on Markowitz’s famous Mean-Variance Portfolio Model (M-V Model), aims at considering Downside Standard Deviation (DSD) and Upside Standard Deviation (USD) respectively and modifying the M-V model to fit the demands of different types of investors. Several well-known stock market indexes over different periods of time are tested to verify the modified models and the performance of the proposed ABC algorithms. The results are also compared with the ones obtained by Variable Neighborhood Search (VNS), Simulated Annealing (SA) and Tabu Search (TS) algorithms in the literatures. The results show that ABC performs better in terms of diversity, convergence, and effectiveness, particularly in ABC II when a Pareto front selection strategy is considered. Thus, ABC in this study is suitable for solving Portfolio Optimization Problem, and is able to provide valuable portfolio for investors with different attributes.

摘 要 i
ABSTRACT ii
致謝 ii
目錄 iv
圖目錄 vii
表目錄 x
第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 2
1.3 研究範圍 3
1.4 研究架構與流程 3
第二章 文獻探討 6
2.1 投資組合最佳化問題（Portfolio Optimization Problem）之探討 6
2.1.1 投資組合理論 6
2.1.2 投資組合最佳化問題之相關研究 6
2.2 人工蜂群演算法（Artificial Bee Colony；ABC）之探討 10
2.2.1 人工蜂群演算法之發展背景 10
2.2.2 人工蜂群演算法之演算方法與基本架構 13
2.2.3 人工蜂群演算法之相關發展與應用 16
2.3 小結 18
第三章 研究方法 19
3.1 投資組合最佳化問題 19
3.1.1 平均數-變異數之受限投資組合最佳化問題 19
3.1.2 下方標準差修正平均數-變異數受限投資組合最佳化問題 20
3.1.3 上方標準差修正平均數-變異數受限投資組合最佳化問題 22
3.1.4修正平均數-變異數受限投資組合最佳化問題 22
3.2 人工蜂群演算法於投資組合最佳化問題之演算架構 23
3.2.1 ABC I之架構 24
3.2.2 ABC II之架構 34
3.3 績效衡量指標 35
第四章 研究結果與分析 40
4.1 測試例題 40
4.2 參數設定 41
4.3 研究結果 42
4.3.1 各演算法於平均數-變異數模型之結果 43
4.3.1.1 測試例題─Hang Seng 43
4.3.1.2 測試例題─DAX 100 47
4.3.1.3 測試例題─FTSE 100 52
4.3.1.4 測試例題─S&P 100 56
4.3.1.5 測試例題─Nikkei 225 61
4.3.2 ABC I與ABC II於下方風險模型之結果 65
4.3.2.1 測試例題─Hang Seng 66
4.3.2.2 測試例題─DAX 100 67
4.3.2.3 測試例題─FTSE 100 68
4.3.2.4 測試例題─S&P 100 69
4.3.2.5 測試例題─Nikkei 225 71
4.3.3 ABC I與ABC II於上方風險模型之結果 72
4.3.3.1 測試例題─Hang Seng 72
4.3.3.2 測試例題─DAX 100 73
4.3.3.3 測試例題─FTSE 100 74
4.3.3.4 測試例題─S&P 100 75
4.3.3.5 測試例題─Nikkei 225 77
4.3.4 不同投資組合股票數（K）於各投資組合模型之結果 78
4.3.4.1 測試例題─Hang Seng 79
4.3.4.2 測試例題─DAX 100 81
4.3.4.3 測試例題─FTSE 100 83
4.3.4.4 測試例題─S&P 100 85
4.3.4.5 測試例題─Nikkei 225 87
第五章 結論與未來研究 89
5.1 結論 89
5.2 未來研究方向 90
參考文獻 91

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