臺灣博碩士論文加值系統

本研究整理了有關不確定性組合之相關文獻，並將文獻所使用的模糊方法分為三類，即模糊決策理論、可能性規劃法、區間規劃法，接著說明解釋各文獻所發展之模型，再從三類模糊方法中各挑選一種模型與傳統的均異模型做比較，並以移動視窗法進行25期的模擬交易測試。實驗結果發現，模糊決策理論建構的模型表現最差，可能性規劃法所建構的悲觀模型則建議在大盤表現不好時採取，區間規劃法所建構的模型不論是在大盤表現好或壞時，樂觀與悲觀模型的表現皆不差。

This study surveys and evaluates related studies in fuzzy portfolio selection. We classify these studies into three categories with the fuzzy approach they employed. These three categories involve fuzzy decision theory, possibilistic programming and interval programming. This study explains the models of these studies, and chooses one model respectively from the three categories to compare with the traditional Markowitz’s mean-variance model. By illustrating selected model with rolling window method, we found the models based on the fuzzy decision theory have worst performance. Besides, the pessimistic models based on possibilistic programming can be selected in bear market, and the pessimistic or optimistic models based on interval programming can be selected in bull market and bear market.

摘要 I
Abstract II
表目錄 IV
圖目錄 V
第一章 緒論 1
1.1 研究背景與動機 1
第二章 文獻探討 3
2.1 不確定性之投資組合 3
2.2 模糊決策理論的模糊投資組合模型 4
2.3 可能性規劃法的模糊投資組合模型 8
2.3.1 中心值-寬度模型 9
2.3.2 利用必然性指標之模型 14
2.4 區間規劃法的模糊投資組合模型 15
2.5 移動視窗分析法 18
第三章 研究方法 19
3.1 模糊投資組合模型之設計 19
3.1.1 基於模糊決策理論的模糊投資組合模型 20
3.1.2 基於可能性規劃法的模糊投資組合模型 21
3.1.3 基於區間規劃法的模糊投資組合模型 22
3.2 均異模型之設計 24
第四章 實證分析 25
4.1資料來源與分析之敘述 25
4.2模擬資料之實作分析 26
4.3實驗 26
第五章 結論與建議 28
參考文獻 30
附錄A 33

I.中文文獻
1.楊敏生，劉曼君 (民85)，「可能性理論淺介」，《數學傳播季刊》，第二十卷第三期。

II.英文文獻
1.R.D. Arnott, and W.H. Wanger, “The measurement and control of trading costs,” Financial Analysts Journal 46 (1990) 73-80.
2.R. Bellman, and L. A. Zadeh, “Decision making in a fuzzy environment,” Management Science, 17 (1970) 141-164.
3.C. Carlsson, and R. Fuller, “On possibilistic mean value and variance of fuzzy numbers,” Fuzzy Sets and Systems, 122 (2001) 315-326.
4.C. Carlsson, R. Fuller, and P. Majlender, “A possibilistic approach to selecting portfolios with highest utility score,” Fuzzy Sets and Systems, 131 (2002) 13-21.
5.L. H. Chen, and L. Huang, “Portfolio optimization of equity mutual funds with fuzzy return rates and risks,” Expert Systems with Application, 36 (2009) 3720-3727.
6.D. Dubois, and H. Prade, Possibility theory, New York, Plenum Press 1988.
7.Y. Fang, K. K. Lai, and S. Y. Wang, Fuzzy portfolio optimization: theory and methods, Berlin, Springer, 2008.
8.Y. Fang, K.K. Lai, and S. Y. Wang, “Portfolio rebalancing model with transaction costs based on fuzzy decision theory,” European Journal of Operational Research, 175 (2006) 879-893.
9.S. Giove, S. Funari, and C. Nardelli, “An interval portfolio selection problem based on regret function,” European Journal of Operational Research, 170 (2006) 253-264.
10.P. Gupta, M. K. Mehlawat, and A. Saxena, “Asset portfolio optimization using fuzzy mathematical programming,” Information Sciences, 178 (2008) 1734-1755.
11.M. Ida, “Portfolio selection Problem with Interval Coefficients,” Applied Mathmetics Letters, (2003) 709-713.
12.P. Jana, T. K. Roy, and S. K. Mazumder, “Multi-objective possibilistic model for portfolio selection with transaction cost,” Journal of Computational and Applied Mathematics, 228 (2009) 188-196.
13.K. K. Lai, S. Y. Wang, J. P. Xu, S. S. Zhu, and Y. Fang, “A class of linear interval programming problems and its application to portfolio selection,” IEEE Transactions on Fuzzy Systems, 10 (2002) 698-704.
14.T. Leon, V. Liern, and E. Vercher, “Viability of infeasible portfolio selection problems: A fuzzy approach, European Journal of Operational Research, 139 (2002) 178-189.
15.H. M. Markowitz, “Portfolio selection,” Journal of Finance, 7 (1952) 77-91.
16.L. Schrage, LINGO Release 8.0, LINDO System, Chiago, 2003.
17.H. Tanaka, and P. Guo, “Portfolio selection based on possibility theory, In: R.A. Ribeiro, H. J. Zimmermann, R. R. Yager, and J. Kacprzyk (Eds.),” Soft Computing in Financial Engineering, Physica-Verlag, Berlin, Heidelberg, (1999) 159-185.
18.H. Tanaka, P. Guo, and I. B. Turksen, “Portfolio selection based on fuzzy probabilities and possibility distributions,” Fuzzy Sets and Systems, 111 (2000) 387-397.
19.E. Vercher, J. D. Bermudez, and J. V. Segura, “Fuzzy portfolio optimization under downside risk measures,” Fuzzy Sets and Systems, 158 (2007) 769-782.
20.E. Vercher, “Portfolio with fuzzy returns: selection strategies based on semi-infinite programming,” Journal of Computational and Applied Mathematics, 217 (2008) 381-393.
21.J. Watada, “Fuzzy portfolio model for decision making in investment, In: Y. Yoshida (Ed.),” Dynamical Aspects in Fuzzy Decision Making, Physica-Verlag, Heidelberg, (2001) 141-162.
22.A. Yoshimoto, “The mean–variance approach to portfolio optimization subject to transaction costs,” Journal of the Operational Research Society of Japan 39 (1996) 99-117.
23.L. A. Zadeh, “Fuzzy sets,” Information and Control, 8 (1965) 338-353.
24.L. A. Zadeh, “Fuzzy sets as a basis for a theory of possibility,” Fuzzy Sets and Systems, 1 (1978) 3-28.
25.W. G. Zhang, “Possibilistic mean-standard deviation models to portfolio selection for bounded assets,” Applied Mathematics and Computation, 189 (2007) 1614-1623.
26.W. G. Zhang, X. L. Zhang, and W. L. Xiao, “Portfolio selection under possibilistic mean-variance utility and a SMO algorithm,” European Journal of Operational Research 197 (2009) 693-700.

III.電子文獻
1.“YAHOO Finance”, http://finance.yahoo.com/
2.“台灣證券交易所”, http://www.twse.com.tw/