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System No. U0002-2407201113263000
Title (in Chinese) 模糊投資組合分析- 模糊報酬與模糊投 資比例的探討
Title (in English) Fuzzy Portfolio Analysis with Fuzzy Returns and Fuzzy Investment Proportion
Other Title
Institution 淡江大學
Department (in Chinese) 管理科學研究所碩士班
Department (in English) Graduate Institute of Management Science
Other Division
Other Division Name
Other Department/Institution
Academic Year 99
Semester 2
PublicationYear 100
Author's name (in Chinese) 廖文督
Author's name(in English) Wen-Du Liao
Student ID 696620037
Degree 碩士
Language Traditional Chinese
Other Language
Date of Oral Defense 2011-06-15
Pagination 56page
Committee Member advisor - Ruey-Chyn Tsaur
co-chair - Ching-Chun Fu
co-chair - Chung-Chu Chuang
Keyword (inChinese) 投資組合理論
模糊理論
演進過程
可能性平均值- 標準差模型
Keyword (in English) portfolio theory
fuzzy theory
the evolution
possibilistic mean-standard models
Other Keywords
Subject
Abstract (in Chinese)
本研究在探討投資者在一個既有的投資組合中,個股投資比例呈現不確定的狀態。首先,本研究從可行性的平均標準差模型,來探討在既有的投資組合中,如何解決個股投資比例的問題。接下來,在既有投資組合中的個股的投資比例的不確定性,將會被視為模糊數,並且會在本研究中被公式化和提出一些可行解。 最後,本研究會沿用一個實例來描述如何用提出的公式來幫助投資者解決在既有的投資組合下,如何分配自有資金進行個股投資比例上的調整的相關問題。
Abstract (in English)
In this paper, the fuzzy portfolio will be discussed due to uncertainty of proportion invested in each selected security in a portfolio. The paper will discuss how to solve the portfolio problem about investment proportion of each selected security based on possibilistic mean-standard deviation models. Then, the uncertain investment proportion of each chosen security in the portfolio will be regarded as a fuzzy number and also be formulated and proposed in this paper, showing how the portfolio selection problem will be solved. Finally, a numerical example of a portfolio selection problem will be shown to illustrate how to deal with it by the mean and the approach the paper presents.
Other Abstract
Table of Content (with Page Number)
致謝	i
中文摘要	ii
Abstract	iii
目錄	iv
表目錄	v
圖目錄	vi

目錄
第一章 緒論	1
第一節 研究背景	1
第二節 研究動機與目的	5
第三節 研究流程	5
第二章 文獻探討	7
第一節 Markowitz的投資組合理論	7
第二節 模糊理論	11
第三節 模糊投資組合相關研究的演進過程	16
第四節 上下界的可能性均值和變異數	19
第五節 可能性平均值-標準差模型	23
第六節 投資組合風險	27
第七節 信用交易與融資	29
第三章 模型建構	30
第一節 投資比例視為模糊數的上下界可能性平均值和變異數	30
第二節 投資比例視為模糊數的可能性平均值-標準差的上下界模型	36
第四章 資料分析	41
第一節 資料說明	41
第二節 上下界的模糊投資比例分析	41
第五章 結論與建議	51
第一節 結論	51
第二節 研究限制與建議	52
參考文獻	54
一、中文文獻	54
二、英文文獻	55

表目錄
表4 - 1 模糊投資組合的上界效率分配 ( 為1.5%)	43
表4 - 2 模糊投資組合的上界效率分配 ( 為3.0%)	43
表4 - 3 模糊投資組合的上界效率分配 ( 為4.5%)	44
表4 - 4 模糊投資組合的下界效率分配 ( 為1.5%)	47
表4 - 5 模糊投資組合的下界效率分配 ( 為3.0%)	47
表4 - 6 模糊投資組合的下界效率分配 ( 為4.5%)	48

圖目錄
圖2 - 1 效率前緣曲線圖	11
圖2 - 2 三角模糊數據隸屬函數圖	15
圖2 - 3 梯形模糊數A的函數圖形	20
圖2 - 4 投資組合的證券數目與風險關係圖	28
References
一、中文文獻
1.徐俊明(2005),五版,投資學─理論與實務。台北市–新陸書局。
2.郝翠翎(2003),「信用交易條件調整對股票市場之影響」,世新大學經濟學研究所碩士論文

二、英文文獻
1. Best M.J., Grauer R.R., The efficient set mathematics when mean–variance problems are subject to general linear constrains, Journal of Economics and Business 42 (1990) 105–120.
2. Best M.J., Hlouskova J., The efficient frontier for bounded assets, Mathematical Methods of Operations Research 52 (2000) 195–212.
3. Burhan T€urksen I., Guo P.,Tanaka H., Portfolio selection based on fuzzy probabilities and possibility distributions, Fuzzy Set and Systems. 111 (2000) 387–397
4. Carlsson C., Fuller R., On possibilistic mean value and variance of fuzzy numbers, Fuzzy Sets and Systems 122 (2001) 315–326.
5. Carlsson C., Fuller R., Majlender P., A possibilistic approach to selecting portfolios with highest utility score, Fuzzy Sets and Systems 131 (2002) 13–21.
6. Chen W., Tan S., On the possibilistic mean value and variance of multiplication of fuzzy numbers, Journal of Computational and Applied Mathematics 232 (2009) 327-334
7. Dubois D., Prade H., Possibility Theory, Plenum Perss, New York, 1988.
8. Funari S., Giove S., Nardelli C., An interval portfolio selection problems based on regret function, European Journal of Operational
Research 170 (2006) 253–264.
9. Guo P.,Tanaka H., Portfolio selection based on upper and lower exponential possibility distributions, European Journal of Operational Research 114 (1999) 115–126.
10. Huang X., Mean-semivariance models for fuzzy portfolio selection, Journal of Computational and Applied Mathematics 217 ( 2008) 1-8
11. Inuiguchi M., Tanino T., Portfolio selection under independent possibilistic information, Fuzzy Sets and Systems 115 (2000) 83–92.
12. Lai K.K., Wang S.Y., et al., A class of linear interval programming problems and its application to portfolio selection, IEEE Transactions on Fuzzy Systems 10 (2002) 698–704.
13. Leon T., Liem V., Vercher E., Viability of infeasible portfolio selection problems: A fuzzy approach, European Journal of Operational Research 139 (2002) 178–189.
14. Lacagnina V., Pecorella A., A stochastic soft constraints fuzzy model for a portfolio selection problem, Fuzzy Sets and Systems 157 (2006) 1317 – 1327
15. Markowitz H., Portfolio selection, Journal of Finance 7 (1952) 77–91.
16. Merton R.C., An analytic derivation of the efficient frontier, Journal of Finance and Quantitative Analysis September (1972) 1851–1872.
17. Nie Z.K., Zhang W.G., On possibilistic variance of fuzzy numbers, Lecture Notes in Artificial Intelligence 2639 (2003) 398–402.
18. Nie Z.K., Zhang W.G., On admissible efficient portfolio selection problem, Applied Mathematics and Computation 159 (2004) 357–371.
19. Nie Z.K., Zhang W.G., et al., Possibilistic mean–variance models and efficient frontiers for portfolio selection problem, Information Sciences 177 (2007) 2787–2801
20. Pang J.S., A new efficient algorithm for a class of portfolio selection problems, Operational Research 28 (1980) 754–767.
21. Perold A.F., Large-scale portfolio optimization, Management Science 30 (1984) 1143–1160.
22. Ramaswamy S., Portfolio Selection Using Fuzzy Decision Theory, Working Paper of Bank for International Settlements, No. 59, 1998.
23. Sharpe W.F., Portfolio Theory and Capital Markets, McGraw-Hill, New York, 1970.
24. Voros J., Portfolio analysis-An analytic derivation of the efficient portfolio frontier, European Journal of Operational Research 203 (1986) 294–300.
25. Watada J., Fuzzy Portfolio Selection and Its Applications to Decision Making, 13, Tatra Mountains Mathematical Publication, 1997, pp. 219–248.
26. Zadeh L.A., ‘Fuzzy Sets,’ Information and Control, 8(1965)338-353
27. Zhang W.G., Possibilistic mean–standard deviation models to portfolio selection for bounded assets, Applied Mathematics and Computation 189 (2007) 1614–1623
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