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研究生:張嘉合
研究生(外文):Chia-Ho Chang
論文名稱:運用馬可夫決策過程作為台灣股市投資決策輔助工具之研究
論文名稱(外文):On Deriving Optimal Stock-Trading Strategies in Taiwan Stock Exchange Market Based on Markov Decision Process
指導教授:姚銘忠姚銘忠引用關係曾宗瑤曾宗瑤引用關係
指導教授(外文):Ming-Jong YaoTsueng-Yao Tseng
學位類別:碩士
校院名稱:東海大學
系所名稱:工業工程與經營資訊學系
學門:工程學門
學類:工業工程學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:英文
論文頁數:62
中文關鍵詞:馬可夫決策過程狀態變數轉移機率矩陣期望利潤線性規劃法門檻值
外文關鍵詞:Markov Decision Processstates variablestransision probability matrixexpected rewardlinear programmingthreshold
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本研究運用馬可夫決策過程數學模式作為投資者投資決策之輔助工具,亦即協助投資者判斷股價變動時應選擇之最佳決策,如買進、賣出、持股續抱、空手觀望…等。研究中運用「胡氏記錄表」定義之狀態變數建立轉移機率矩陣,並考量近期內狀態變數之轉移機率提供投資者趨勢之訊息應較顯著,以近期歷史資料建立不可約馬可夫鏈中之轉移機率矩陣,接著以線性規劃法求解最佳交易決策,並運用門檻值及狀態變數數列修正交易法則。本研究以110支上市股票於民國95年1月至民國96年3月進行實務驗證,說明透過本研究提出之交易法則可有效輔助投資者進行股票交易之決策,獲得合理報酬。
In this study we derive optimal stock-trading strategies in Taiwan stock exchange market (TSEM) based on Markov Decision Process (MDP). First, we defined the 14 states variables in the MDP that match with the 7%-limit rule on the stock-price change in TSEM. According to historical price data at the end of each trading day, we set up the transition probability matrix for a particular stock. For each state, we defined two decisions in the MDP model, namely, either buy-in or sell-out only one unit (1,000 shares) of the stock. We calculated the expected reward for the two decisions in each state using the historical price data and obtained the optimal decision in each state by solving a linear program corresponding to the MDP model. Also, we proposed two stock-trading rules that modified the optimal strategy from the MDP model by incorporating with the rules of threshold conditions and state-variable sequence patterns. We verified the effectiveness of our optimal strategies by 110 stocks in TSEM using the real data from January of 2005 to March of 2006. We demonstrated that our optimal trading strategies out-perform other commonly-used trading strategies.
ABSTRACT i
Table of Contents ii
List of Tables iv
List of Figures v
Chapter 1 Introduction 1
1.1 BACKGROUND AND MOTIVATION 1
1.2 SCOPE AND LIMITATIONS 2
1.3 IMPLEMENTATION STEPS 2
Chapter 2 Literature Review 4
2.1 MARKET EFFICIENCY ASSUMPTION 4
2.2 PREDICTION AND DECISION-MAKING ANALYSIS METHODS 5
2.2.1 Fundamental Analysis 5
2.2.2 Technical Analysis 5
2.2.3 Neural Network and Neural-Fuzzy System 6
2.2.4 Expert System 7
2.3 RESEARCH GAPS 7
Chapter 3 The Proposed Heuristic Baesd on MDP 9
3.1 THE PROPOSED MATHEMATICAL MODEL 9
3.1.1 Hu’s Log and Definition of State Variable 9
3.1.2 The Setup of the Transition Probability Matrix 10
3.1.3 The Definition of the Decision Variables 11
3.1.4 The Calculation of the Observation Duration 12
3.1.5 The Expected Reward 13
3.2 SOLVING THE OPTIMAL TRADING DECISION 14
3.2.1 Linear Programming 14
3.2.2 Solving the Optimal Trading Decision Based on the Expected Reward 15
3.2.3 The Modified Trading Heuristic Rule Using a Upper and a Lower Threshold 17
3.2.4 The Modified Trading Heuristic Rule Using the Series of the State Variables 17
Chapter 4 Verification Using Real-world Data 19
4.1 ANALYSIS ON THE RETURN OF INVESTMENT 20
4.2 ANALYSIS ON THE ARRIVAL TIME OF THE STATE VARIABLES 21
4.3 ANALYSIS ON THE ENVIRONMENT OF STOCK MARKET 23
4.4 COMPARISON WITH THE K-LINE APPROACH 25
4.5 ANALYSIS ON THE SECURITIES FUNDS 26
Chapter 5 Conclusions and Extensions 28
References 29
Appendix A.1 Brief Introduction of Markov Decision Process 32
A.1.1 THE MATHEMATICAL MODEL 32
A.1.2 POLICY ITERATION 33
A.1.3 VALUE ITERATION 35
A.1.4 LINEAR PROGRAMMING 36
A.1.5 COMPARISON OF THE APPROACHES FOR SOLVING THE MDP 37
Appendix A.2 Hu’s Log and Its Book-keeping Rules 38
Appendix A.3 The Setup of the Transition Probability Matrix 45
Appendix A.4 The Calculation of the Observation Duration 48
Appendix A.5 The Calculatin of the Expected Reward 57
Appendix A.6 The Calculation of the Treshold 59
Appendix A.7 The Calculation of the Series of the State Variables 61
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