臺灣博碩士論文加值系統

對於不斷變化的實際資產市場，投資者對於資產及其相關面象的變化只能以語意描述其模糊的信息。因此，想獲得報酬率的精確機率分佈並不容易，針對此類問題，相關學者建議使用模糊集理論作為替代方法，來求解最佳的投資組合。有鑑於此，本研究規劃兩個研究議題。
首先，對不穩定的、模糊報酬相關的最佳投資組合選擇方法，提出一個模糊投資組合模型。本文嘗試引介一種新的模糊報酬函數——基於報酬的選擇保證率，將某些證券放在超額投資的框架下來討論——來改善可能平均值與變異值，導向一種改良的模糊組合分析模型。本文驗證前述模型在不同的投資風險下，設定最低保證報酬率的期望投資報酬率，是大於較高保證報酬率的期望投資報酬率。這個投資組合分析可以提供一個更有貢獻的投資選擇。其次，在不穩定或模糊的報酬中，本文提出了另一個模糊的投資組合模型作為最佳投資組合選擇方法。
雖然許多論者已經戮力於研究模糊的投資組合模型，在模糊投資組合模型中，設定可調式證券比例以探討投資保證率的超額投資與缺額投資。為了處理這樣的投資，我們根據最低報酬保證率假設某些證券被考量超額投資而某些證券被考量為缺額投資。研究範例顯示在不同等級的投資風險下，較低的報酬保證率的期望報酬率是高於較高的報酬保證率的期望報酬率的，而在較高的投資風險下，投資報酬率低的證券的投資比率是幾近於零。

For the changing asset market, investors can only use Linguistic description to describe the vague information of the changes in assets and related aspects. Therefore, it is not easy to obtain an accurate probability distribution of the rate of return. For such problems, relevant scholars suggest using fuzzy set theory as an alternative method to solve the best investment portfolio. Therefore, this research plans two research topics. First, a fuzzy investment portfolio model is proposed for the optimal portfolio selection related to unstable and fuzzy returns. This article attempts to introduce a new fuzzy return function based on the selection guarantee rate of return, some securities are discussed in the framework of excess investment to improve the possible average value and variance value, leading to an improved fuzzy combination analysis model. This article proves that under different investment risks, the proposed model sets the expected ret
urn on investment with a lower guaranteed rate of return, which is greater than the expected return on investment with a higher guaranteed rate of return. This portfolio analysis can provide a more contributory investment option. Secondly, in the unstable or fuzzy returns, this paper proposes another fuzzy portfolio model as the best investment portfolio selection method. Although many commentators have worked hard to study the fuzzy portfolio model, in the fuzzy portfolio model, the adjustable securities ratio is set to explore the excess investment and the short investment of the guarantee rate of return. In order to deal with such investments, we assume that certain securities are considered excess investment and certain securities are considered short investment based on the guaranteed rate of return. The illustration shows that under different levels of investment risk, the expected return rate of a lower guarantee rate of return is higher than the expected return rate of a hig
her guarantee rate of return. With higher investment risks, the ratio of securities investment with low return on investment is almost zero.

誌謝 Ⅰ
中文摘要 Ⅱ
英文摘要 Ⅲ
目錄 Ⅴ
表目錄 Ⅵ
圖目錄 Ⅶ

第一章 前言 1
1.1 動機與目的 2
1.2 論文結構 4
第二章 模糊投資組合文獻及模式回顧 5
2.1 文獻探討 5
2.2 模糊數算術運用 7
2.3 模糊的投資組合模型 10
第三章 可調整式的模糊投資組合模式 15
3.1 基於保證報酬率的模糊投資組合模型 15
3.2 證券比率可調整的模糊投資組合 19
第四章 模型驗證 25
4.1 基於保證報酬率的模糊投資組合範例 25
4.1.1 範例步驟 27
4.1.2 保證報酬率模型與其他模型的比較分析 34
4.2 證券投資比率可調整的模糊投資組合範例 36
第五章 結論 43
5.1 研究成果 43
5.2 管理意涵 44
5.3 未來研究 45
參考資料 47
表目錄
表 4- 1 保證報酬率1~p的可能最佳投資組合................. 29
表4- 2 保證報酬率2~p的可能效率投資組.................... 31
表4- 3 保證報酬率3~p的可能效率投資組合.................. 31
表4- 4 混合保證報酬率的可能最佳投資組合................. 33
表4- 5 模糊投資組合模型的比較.......................... 35
表4- 6 每個選擇證券的模糊報酬.......................... 37
表4- 7 保證報酬率為1~p時的可能最佳投資組合.............. 39
表4- 8 保證報酬率為2~p時的可能最佳投資組合.............. 40
表4- 9 保證報酬率為3~p時的可能最佳投資組合.............. 42
圖目錄
圖 4- 1 不同保證報酬率的投資組合比較分析................ 32

[1].Bawa, V. S. , Lingenberg, E. B. (1977). Capital Market Equilibrium in A Mean-Lower Partial Moment Framework. Journal of Financial Economics, 5, 189–200.
[2].Bazaraa, M. S., Jarvis, J. J., Sherali, H. D. (1990). Linear Programming and Network Flows (2nd ed.). New York: Wiley.
[3].Berman, O., Sanajian, N., Wang, J.O. (2017). Location Choice and Risk Attitude of a Decision Maker. Omega, 66, 170–181. 

[4].Best, M. J., Grauer, R. R. (1990). The Efficient Set Mathematics when Mean–Variance Problems are Subject to General Linear Constrains. Journal of Economics and Business, 42, 105–120.
[5].Best, M. J., Hlouskova, J. (2000). The Efficient Frontier for Bounded Assets. Mathematical Methods of Operations Research, 52, 195–212.
[6].Campbell, R., Huisman, R. , Koedijk , K. (2001). Optimal Portfolio Selection in a Value-at-Risk Framework. Journal of Banking and Finance, 25, 1789-1804.
[7].Carlsson, C., Fulle′r, R. (2001). On Possibilistic Mean Value and Variance of Fuzzy Numbers. Fuzzy Sets and Systems, 122, 315–326.
[8].Chang, P. T., Lee, E. S. (1994). Ranking of Fuzzy Sets Based on the Concept of Existence. Computers and Mathematics with Applications, 27, 1–21.
[9].Chen, W., Di, L., Liu, Y. (2018). A Novel Hybrid ICA-FA Algorithm for Multiperiod Uncertain Portfolio Optimization Model Based on Multiple Criteria. IEEE Transaction Fuzzy Systems, 27, 1023–1036.
[10].Chen, I. F., Tsaur, R. C. (2016). Fuzzy Portfolio Selection Using a Weighted Function of Possibilistic Mean and Variance in Business Cycles. International Journal of Fuzzy Systems,18, 151–159.
[11].Chen, S. H. (1985). Ranking Fuzzy Numbers with Maximizing Set and Minimizing Set. Fuzzy Sets and Systems, 17, 113–129.
[12].Deng, Y., Zhenfu, Z., Qi, L. (2006). Ranking Fuzzy Numbers with an Area Method Using Radius of Gyration. Computers and Mathematics with Applications, 51, 1127–1136.
[13].Guo, S., Yu, L., Li, X., Kar, S. (2016). Fuzzy Multi-Period Portfolio Selection with Different Investment Horizons. European Journal of Operational Research, 254, 1026–1035.
[14].Gupta, P., Mehlawat, M. K., Yadav, S., Kumar, A. (2019). A Polynomial Goal Programming Approach for Intuitionistic Fuzzy Portfolio Optimization Using Entropy and Higher Moments. Applied Soft Computing, 85, 105781.
[15].Huang, X. (2008). Mean-Semivariance Models for Fuzzy Portfolio Selection. Journal of Computational and Applied Mathematics, 217, 1–8.
[16].Jain, R. (1985). Decision Making in the Presence of Fuzzy Variables. IEEE Transactions on Systems, Man and Cybernetics, 6, 698–703, 1976.
[17].Konno, H. , Yamakazi, H. (1991). Mean-Absolute Deviation Portfolio Optimization Model and its Applications to the Tokyo Stock Market. Management Science, 3, 519–531.
[18].Lee, C. L. (2007). The Strengths and Limitations of Risk Measures in Real Estate: A Review. Malaysian Journal of Real Estate, l, 68–74.
[19].Li, X., Qin, Z., Kar, S. (2010). Mean-Variance-Skewness Model for Portfolio Selection with Fuzzy Returns, European Journal of Operational Research 202 239–247.
[20].Liagkouras, K., Metaxiotis, K. (2018). Multi-Period Mean–Variance Fuzzy Portfolio Optimization Model with Transaction Costs, Engineering Applications of Artificial Intelligence, 67, 260–269.
[21].Liu, C., Zheng, H. (2016). Asymptotic Analysis for Target Asset Portfolio Allocation with Small Transaction Costs. Insurance: Mathematics and Economics, 66 59–68. 

[22].Mansour, N., Cherif, M. S., Abdelfattah, W. (2019). Multi-Objective Imprecise Programming for Financial Portfolio Selection with Fuzzy Returns. Expert Systems with Applications, 138, 112810.
[23].Markowitz, H. (1952). Portfolio Selection. Journal of Finance, 7, 77–91.
[24].Merton, R. C. (1972). An Analytic Derivation of the Efficient Frontier. Journal of Finance and Quantitative Analysis, 10, 1851–1872.
[25].Mittal, S. K., Srivastava, N. (2021) Mean-Variance-Skewness Portfolio Optimization under Uncertain Environment Using Improved Genetic Algorithm. Artificial Intelligence Review
[26].Pang, J. S. (1980). A New Efficient Algorithm for a Class of Portfolio Selection Problems. Operational Research, 28, 754–767.
[27].Perold, A. F. (1984). Large-Scale Portfolio Optimization. Management Science, 30, 1143–1160.
[28].Rao, P. P. B., Shankar, N. R. (2011). Ranking Fuzzy Numbers with a Distance Method Using Circumcenter of Centroids and an Index of Modality. Advances in Fuzzy Systems, 2011, Article ID 178308, doi:10.1155/2011/178308.
[29].Saade, J. J, Schwarzlander, H. (1992). Ordering Fuzzy Sets Over the Real Line: an Approach Based on Decision Making under Uncertainty. Fuzzy Sets and Systems, 50, 237–246.
[30].Sharpe, W. F. (1970). Portfolio Theory and Capital Markets. McGraw-Hill, New York.
[31].Tanaka, H., Guo, P. (1999). Portfolio Selection Based on Upper and Lower Exponential Possibility Distributions. European Journal of Operational Research, 114, 115–126.
[32].Tanaka, H., Guo, P., Türksen, I. B. (2000)., Portfolio Selection Based on Fuzzy Probabilities and Possibility Distributions. Fuzzy Set and Systems, 111, 387–397.
[33].Tansakul, N., Yenradee, P. (2020). Fuzzy Improvement-Project Portfolio Selection Considering Financial Performance and Customer Satisfaction. International Journal of Knowledge and Systems Science, 11, 41–70.
[34].Tsaur, R. C. (2013). Fuzzy Portfolio Model with Different Investor Risk Attitudes. European Journal of Operational Research, 227, 385–390.
[35].Tsaur, R. C. (2015). Fuzzy Portfolio Model with Fuzzy-Input Return Rates And Fuzzy-Output Proportions. International Journal of Systems Science, 46, 438–450.
[36].Tsaur, R. C. , Chiu, C. L., Huang, Y. Y. (2021). Fuzzy Portfolio Selection in COVID-19 Spreading Period Using Fuzzy Goal Programming Model. Mathematics, 9, 835.

[37].Vörös, J. (1986). Portfolio Analysis-An Analytic Derivation of the Efficient Portfolio Frontier. European Journal of Operational Research, 203, 294–300.
[38].Wang, Z. X., Mo, Y. N. (2010). Ranking Fuzzy Numbers Based On Ideal Solution. Fuzzy Information and Engineering, 2, 27–36.
[39].Wei Y., Wang Y., Xuan H. (2019). Fuzzy Multi-Objective Portfolio Model Based On Semi-Variance-Semi-Absolute Deviation Risk Measures. Soft Computing, 23, 8159–8179.
[40].Zadeh, L. A. (1965). Furzy Sets. Information Control, 8, 338–353.
[41].Zhang, P. (2018). Multiperiod Mean Absolute Deviation Uncertain Portfolio Selection. Soft Computing, 15, 1–18.
[42].Zhang, W. G. (2007). Possibilistic Mean–Standard Deviation Models To Portfolio Selection For Bounded Assets. Applied Mathematics and Computation, 189, 1614–1623.
[43].Zhang, W. G., Nie, Z. K. (2003). On Possibilistic Variance Of Fuzzy Numbers. Lecture Notes in Artificial Intelligence, 2639, 398–402.
[44].Zhang, W., Nie, Z. (2004). On Admissible Efficient Portfolio Selection Problem. Applied Mathematics and Computation, 159, 357–371.
[45].Zhou, W., Xu, Z. (2018). Portfolio Selection And Risk Investment Under The Hesitant Fuzzy Environment. Knowledge-Based Systems, 144, 21–31.
[46].Zhou, X., Wang, J., Yang, X., Lev, B., Tu, Y., Wang, S. (2018). Portfolio Selection Under Different Attitudes In Fuzzy Environment. Information Sciences, 462, 278–289.