政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/32556

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/32556

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政大典藏 > College of Science > Department of Mathematical Sciences > Theses > Item 140.119/32556

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/32556

Title:	大中取小法建立最佳投資組合 Portfolio Optimization Using Minimax Selection Rule
Authors:	楊芯純 Shin-Chuen Yang
Contributors:	劉明郎楊芯純 Shin-Chuen Yang
Keywords:	大中取小原則投資組合優化混合整數線性規劃 mini-max principle portfolio optimization mixed integer linear program
Date:	2002
Issue Date:	2009-09-17 13:44:38 (UTC+8)
Abstract:	本文提出一個新的混合整數線性規劃模型建立投資組合。這個模型所採用的風險函數為最大損失的絕對值，而不是一般常用的損失變異數。在給定的報酬水準下，模型尋找在觀測期間中最小的最大損失的投資組合，即為大中取小的原則。模型也同時考慮實務上常遇見之情況，如：交易成本、最小交易單位、固定交易費用比率、資產總類數等限制。因此，模型內需使用整數變數及二元變數，導致模型的計算求解過程變得比不含整數變數及二元變數的模型困難許多。我們以固定整數變數的啟發式演算法增進求解的效率，並以台灣股票市場的資料做為實證計算的對象。 A new mixed integer linear program (MILP) for selecting portfolio based on historical return is proposed. This model uses the downside risk rather than the variance as a risk measure. The portfolio is chosen that minimizes the maximum downside risk over all past observation periods to reach a given return level. That is a mini-max principle. The model incorporates the practical characteristics such as transaction costs, minimum transaction units, fixed proportional transaction rates, and cardinality constraint. For this reason a set of integer variables and binary variables are introduced. The introduction, however, increases the computational complexity in model solution. Due to the difficulty of the MILP problem, a heuristic algorithm has been developed for the solution. The computational results are presented by applying the model to the Taiwan stock market.
Reference:	Brooke, A., D. Kendrick, and A. Meeraus, GAMS-A User’s Guide, The Scientific Press, Redwood City, CA (1988). Cai, X., K. L. Teo, X. Yang and X. Y. Zhou, Portfolio optimization under a minimax rule, Management Science 46, 957-972 (2000). Feinstein, C. D. and M. N. Thapa, A reformulation of a mean-absolute deviation portfolio optimization model, Management Science 39, 1552-1553 (1993). Ghezzi, L. L., A maxmin policy for bond management, European Journal of Operational Research 114, 389-394 (1999). IBM, Optimization Subroutine Library Guide and Reference Relese 2, Kingston, NY, Third Edition, (1991). Konno, H. and H. Yamazaki, Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market, Management Science 37, 519-531 (1991). Konno, H. and A. Wijayanayake, Portfolio optimization problem under concave transaction costs and minimal transaction unit constraints, Mathematical Programming, Series B 89, 233-250 (2001). Lee, S. M. and D. L. Chesser, Goal programming for portfolio selection, The Journal of Portfolio Management Spring, 22-26 (1980). Mansini, R. and M. G. Speranza, Heuristic algorithms for the portfolio selection problem with minimum transaction lots, European Journal of Operational Research 114, 219-233 (1999). Markowitz, H., Portfolio selection, Journal of Finance 7, 77-91 (1952). Markowitz, H., Portfolio selection (2nd ed.), Blackwell, Cambridge, MA(1991). Meade, N. and G. R. Salkin, Index funds-construction and performance measurement, Journal of the Operational Research Society 40, 871-879 (1989). Sharpe, W. F., A linear programming algorithm for mutual fund portfolio selection, Management Science 13, 499-510 (1967). Sharpe, W. F., A linear programming approximation for the general portfolio analysis problem, Journal of Financial and Quantitative Analysis December, 1263-1275 (1971). Speranza, M. G., Linear programming models for portfolio optimization, Finance 14, 107-123 (1993). Speranza, M. G., A heuristic algorithm for a portfolio optimization model applied to the Milan stock market, Computers & Operations Research 5, 433-441 (1996). Xia, Y., B. Liu, S. Wang and K. K. Lai, A model for portfolio selection with order of expected returns, Computers & Operations Research 27, 409-422 (2000). Young, M. R., A minimax portfolio selection rule with linear programming solution, Management Science 44, 673-683 (1998). Yu, G., Min-max optimization of several classical discrete optimization problems, Journal of Optimization Theory and Applications 98, 221-242 (1998). 呂建鴻，考量下層風險的最佳投資組合，國立政治大學應用數學研究所碩士論文（民91）。
Description:	碩士國立政治大學應用數學研究所 89751003 91
Source URI:	http://thesis.lib.nccu.edu.tw/record/#G0089751003
Data Type:	thesis
Appears in Collections:	[Department of Mathematical Sciences] Theses

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