二階段隨機規劃模式於投資組合策略之應用

Application of Two-Stage Stochastic Linear Programming for Portfolio Selection Problem

林靜芬(Ching-Fen Lin)

指導教授 ： 張國華

中原大學/工學院/工業工程研究所/碩士(2005年)

https://doi.org/10.6840/cycu200500228

摘要

隨著金融市場之自由化、國際化及多元化，加上衍生性金融商品相繼推出， 提供投資人有更多的投資機會。但也由於投資工具的複雜，選擇投資組合之問題 愈益成為一重要之議題。 本論文利用期貨與股票的反向持有來尋求可動態結算下之最佳投資組合。我 們的投資策略為於每個交易月期初，買進股票之投資組合並賣空期貨，在交易期 間若報酬超過所預定之門檻值，則進行結算。 由於結算時間的不確定性，我們建立一個二階段隨機規劃( two-stage SLP) 之數學模式以尋求在考慮可動態結算下之最佳投資組合。在第一階段，利用 safety-first 找出一投資組合，而將由於期中結算時間不確定性而所獲之利潤交由 第二階段計算。最後利用歷史資料驗證我們所選取之投資組合的利潤較為穩定且 高於定存，並獨立於市場。

關鍵字

投資組合 ； 二階段隨機規劃模式 ； 期貨

並列摘要

In this thesis, a portfolio selection problem with closing the portfolio dynamically
is considered. The investment strategy is to take the long position on the stocks
and the short position in the index futures which starts from the first date when the
futures is issued and ends once the revenue exceeds the predetermined threshold which
is thought as both fixed and dynamic during the investment period. If the profit is
always unable to exceed the threshold during the investment period, all positions will
be closed on the maturity date of the futures.
To deal with the uncertainty on closing date of the portfolio, it is modeled
as a two-stage stochastic linear programming (two-stage SLP). In the first stage of
this SLP, a portfolio is obtained under the safety-first criterion; the second stage
determines the extra revenue of this given portfolio if it ends during the investment
period. The results will be verified by the real-world data and the purpose is to show
that the return of the portfolio is steady, profitable and independent of the market.
Keywords: Portfolio selection, Futures, Two-stage stochastic linear program.

並列關鍵字

Futures ； Portfolio selection ； Two-stage stochastic linear programming

參考文獻

[2] Caroe, C. C., Schultz, R. (1999) ”Dual decomposition in stochastic integer programming”,

Operations Research Letters, Vol. 24, 37-45.

[4] Chang, K. H., Chen, H. J., Liu, C. Y. (2002) ”A stochastic programming model

[5] Elton, E. J., Gruber, M. J. (1995) Modern Portfolio Theory and Investment

Analysis, John Wiley and sons, New York.