未知動態系統之模糊決策研究：以最佳投資組合為例

Fuzzy Decision for Unknown Dynamic Systems: A Portfolio Example

李健祺(Chien-Chi Li)

指導教授 ： 練光祐

國立臺北科技大學/電資學院/電機工程系研究所/碩士(2009年)

摘要

針對未知的動態方程系統，本論文探討如何運用有限的未來訊息，求解系統的最佳化問題，而投資組合即為此典型問題。在此，我們視未來市場趨勢為未知動態方程的有限訊息，從而建構一個使成本函數最大化的決策問題。從這個最佳化問題的架構中，我們目標是找出投資組合的最佳配置方式，使得在未來每一期結束後，目標函數在有限的風險下將會有最大的報酬。在投資組合的應用中，對投資組合的未來動態序列是難以得知的。不過，選擇權市場的Black-Scholes評價公式可用來修正未來的動態序列。這是因為選擇權市場與現貨市場是息息相關的。有價證卷的許多隱藏訊息可藉由其對應的選擇權價格求得。投資人便可從隱含波動率和未平倉量來觀察股票價格的未來走勢。我們建立一個資產配置問題的模糊決策器，來改良傳統的Markowitz投資組合。在一個完善的決策中，若能避免期望報酬與風險被高估或低估，便能建構出最佳的投資組合配置。在數值模擬的部分，我們提出的數種投資組合模型中，本論文最後提出的決策架構可得較佳的投資獲利。

關鍵字

Markowitz投資組合 ； Black-Scholes 模型 ； 隱含波動率 ； 投資組合動態方程

並列摘要

Considering a system with unknown dynamics, we investigate the decision making problem which maximizes a cost function from a given partial known future trend sequence. After set up the framework of such an optimization problem, we focus on how to determine an optimal sequence of portfolio adjustments, and the purpose is maximizing a utility function at the end of some periods. At the portfolio application, it is crucial to identify the future dynamic series of the portfolio composition. To this end, the well-known Black-Scholes pricing formula for option market is used to modify the future dynamic series. This is because the option market, and the spot market will be closely and affect each other. Many implicit messages of stocks can be obtained through examining their options. From the implied volatility, and the open interest that the investors’ viewpoints will see trend of the stock prices in the future trend can be extracted. Then, it can improve the conventional Markowitz portfolio to establish a one-period and a multi-period fuzzy decision makers. Since the phenomenon of overestimation and underestimation for expected return and risk can be avoided, the more reliable future dynamic series of the portfolio composition are obtained, which results in a better decision making. Numerical examples also show among several portfolio models, the proposed decision-making scheme exhibit the highest profit for asset allocation.

並列關鍵字

Markowitz Portfolio Theory ； Black-Scholes Model ； Implied Volatility ； Portfolio Dynamics

參考文獻

[1] J. Hull, Options, Futures, and Other Derivatives, 3rd Ed., Prentice Hall International, 1997.

[4] H. M. Markowitz, “Portfolio Selection,” Journal of Finance, vol. 7, 1952, pp. 77-91.

[5] F. Black and M. Scholes, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, vol. 81, 1973, pp. 637-654.

[6] G. Gemmill, “The Forecasting Performance of Stock Options on the London Traded Options Market,” Journal of Business Financeand Accounting, vol. 3, 1986, pp. 535-546.

[7] J. C. Cox, S. A. Ross, and M. Rubinstein, “Option Pricing: A Simplified Approach,” Journal of Financial Economics, vol.7, 1979, pp. 229-263.