由於金融市場對我們生活中的事件具有敏感性，投資組合選擇將會是一個優化問題。過去的許多研究已經提出了許多最佳化方法來推導出不同類型的投資組合，而其中一種即是群組股票投資組合。群組股票投資組合可以在投資者做決策時，提供更有用的投資組合。然而，其中的大多數方法都專注於單時期投資組合的最佳化。在本文中，我們首先提出了一個多時期群組股票投資組合的最佳化框架。根據所提出的框架，我們提出了一種基於分組遺傳的算法，以獲得多時期的群組股票投資組合。通過四個部分：股票歸屬、股票分組、組可用性和權重，將多時期群組股票投資組合編碼到染色體之中。算法中的每條染色體將通過三個因子來進行適合度評分，而這些因子分別為：累進回報因子，累進安全性因子和投資風格因子。除此之外，一個非支配集合池將在演化過程中不斷地被更新與維護，藉此增加母體的多樣性。維護此非支配集合池亦可以在演化計算的最終階段提供更高品質的解。然而，如果算法中待計算的股票數量龐大時，所提出的算法對於多時期群組股票投資組合的最佳化計算將會變得非常耗時。為了增強算法使其減輕運算耗時的問題，一個新的染色體編碼方式亦被設計並提出。本論文亦在三個金融數據集上進行實驗，以顯示所提出方法的優點。

Portfolio selection is an optimization issue due to the sensitivity of financial markets to the occurrences around our lives. Lots of optimization methods have been proposed to derive different types of portfolios. A type of them is the group stock portfolio which can provide a more useful portfolio for investors making decisions. However, most of them focus on the single-period portfolio optimization. In this thesis, we present a multi-period group stock portfolio optimization frame-work firstly. Then, based on the presented framework, we thus propose an algorithm to obtain a multi-period group stock portfolio based on using the grouping genetic algorithm is proposed. It encodes a multi-period group stock portfolio into a chromosome by the belonging, grouping, group availability and weight parts. Every chromosome is then evaluated by three factors: the accumulated return, the accumulated safety, and the investment style factors. A front pool which is a set of non-dominated solutions is also maintained to enhance the diversity of the population. It also leads to a higher quality of discovered solutions in the final stage. Be-cause the proposed algorithm is time-consuming for optimizing a multi-period group stock portfolio when the number of stocks is large, the enhanced algorithm is then designed to solve it by a new chromosome encoding method. Experiments were also conducted on the three financial datasets to show the merits of the pro-posed approach.

Contents
Chapter 1	Introduction	1
1.1	Introduction	1
1.2	Contribution	3
1.3	Reader’s Guide	3
Chapter 2	Problem Definition and Related Work	4
2.1	GGA and Grouping Problems	4
2.2	Problem Definition	5
2.3	Review of Single-Period Stock Portfolio Optimization Approaches	6
2.4	Review of Multi-Period Stock Portfolio Optimization Approaches	8
Chapter 3	Multi-period Group Stock Portfolio Optimization Approach	10
3.1	Motivation	10
3.2	The Multi-Period GSP Optimization Framework	14
3.3	Elements of the Proposed Algorithm	16
3.3.1	Encoding Scheme	17
3.3.2	Fitness Evaluation	18
3.3.3	Genetic Operations	23
3.3.4	Selection	26
3.4	Proposed Algorithm	28
3.5	Enhancement of Approach in Efficiency	29
3.6	An Example for Fitness Evaluation	30
3.6.1	Accumulated Return Factor	33
3.6.2	Accumulated Safety Factor	36
3.6.3	Investment Style Factor	40
3.6.4	Factors combination	43
Chapter 4	Experimental Results	44
4.1	Parameter setting	44
4.2	Dataset Description	45
4.3	Evaluation in Terms of Returns	47
4.4	Evaluation in Terms of Execution Time	51
4.5	Evaluation in Terms of Different Parameter Settings	52
4.6	The Effectiveness of the Front Pool	53
4.7	The Derived Multi-Period GSP	55
Chapter 5	Conclusion and Future Works	57
References	59

List of Figures
Figure 1. Stock prices of 2886 (TW) in 2018.	11
Figure 2. An example of the explanation for the difference between the multi-period portfolio and the continuous single-period portfolio.	14
Figure 3. The proposed framework.	15
Figure 4. The encoding schema to represent a multi-period GSP.	17
Figure 5. The pseudo code of the proposed approach	28
Figure 6. The modified encoding scheme for the enhanced approach.	30
Figure 7. The example dataset	31
Figure 8. The buy prices of the 7 example companies in each period.	31
Figure 9. An example GSP chromosome	32
Figure 10. Extract the combination from the example GSP chromosome	32
Figure 11. The example for calculating the accumulable RoI table.	33
Figure 12. The calculation of the accumulated return for each combination.	34
Figure 13. The results of the accumulated return for each combination.	35
Figure 14. The difference table of the 7 example companies for VaR calculation.	36
Figure 15. The difference table in ratio of the 7 example companies for VaR calculation.	37
Figure 16. The safety table of the 7 example companies.	37
Figure 17. The calculation of accumulated safety.	38
Figure 18. The results of accumulated safety for each combination.	39
Figure 19. The example of group balance calculation.	40
Figure 20. The example of the weight balance calculation.	41
Figure 21. The example of the portfolio size penalty calculation.	41
Figure 22. The example of the starting capital bias penalty calculation.	42
Figure 23. The combination of investment style factor.	43
Figure 24. The example of factors combination.	43
Figure 25. The real dataset of 15 stocks.	45
Figure 26. The real dataset of 30 stocks.	46
Figure 27. The real dataset of 53 stocks.	46
Figure 28. The average fitness values of the proposed approach with/without the front pool.	53

List of Tables
Table 1. RoI of 2886 (TW) for single-period/multi-period investment.	12
Table 2. The average of ten times accumulated returns of the proposed approach and the BHS with the fifteen stocks and six periods	47
Table 3. The average of ten times accumulated returns of the proposed approach (P=6) and the single period with the fifteen stocks.	48
Table 4. The average of ten times accumulated returns of the proposed approach and the BHS with the thirty stocks and six periods	48
Table 5. The average of ten times accumulated returns of the proposed approach (P=6) and the single period with the thirty stocks.	49
Table 6. The average of ten times accumulated returns of the proposed approach and the BHS with the fifty-three stocks and six periods	49
Table 7. The average of ten times accumulated returns of the proposed approach (P=6) and the single period with the fifty-three stocks.	50
Table 8. The average execution time of the proposed approach compared to the single-period.	51
Table 9. The Effects when changing the crossover rate (mutation rate: 0.3 ~ 0.1)	52
Table 10. The Effects when changing mutation rate (crossover rate: 0.8 ~ 0.5)	52
Table 11. The derived multi-period GSP	55

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