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研究生:李易昀
研究生(外文):I-Yun Lee
論文名稱(外文):Optimal Strategies for Index Tracking with Risky Constrains
指導教授:孫立憲孫立憲引用關係
學位類別:碩士
校院名稱:國立中央大學
系所名稱:統計研究所
學門:數學及統計學門
學類:統計學類
論文出版年:2020
畢業學年度:108
語文別:英文
論文頁數:54
中文關鍵詞:市場追蹤最佳化投資策略動態編程原理哈密頓-雅可比-貝 爾曼方程二次逞罰方程
外文關鍵詞:Market trackingportfolio optimizationdynamic programming principleHamilton–Jacobi–Bellman equationexact penalty function
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指數追蹤在金融市場中是一種很流行的被動投資策略,追蹤問題是 藉由選取目標指數內含的股票種類所建立的資產組合來複製目標指數的 動向。此篇文章主要透過優化控制問題的方法建構模型來處理指數追蹤, 找出最佳化策略並提供證明。然而,追蹤指數時存在追蹤不穩定的問題, 當追蹤不穩定的情形發生時會造成過大的追蹤誤差。此研究中特地加入 對風險性資產的二次逞罰項及探討追蹤不穩定的情形,來減弱控制追蹤 不穩定的情形發生時造成過多的追蹤誤差。在實證研究中,使用 S&P 500 和美國股票顯示所提出的模型控制了追蹤的不穩定性,並且與無控 制風險的策略比較追蹤表現。
Index tracking is a popular passive investment strategy in finance. It refers to the problem of reproducing the performance of a stock market index by considering a portfolio of assets comprised on the index. This paper mainly attempts to construct a model based on the technique of the portfolio optimization problem through the linear quadratic regulator to trace closely an index. We obtain the optimal strategy using the dynamic programming and the corresponding HJB equation. However, we consider the problem of tracking instability when tracking the index through portfolio optimization. In this case would cause the excessive tracking error. Therefore, this research specifically joins the penalty quadratic term in risky assets and attempts to capture the tracking of unstable situations to weaken the tracking error. We show that the proposed model controls the tracking instability and compare the performance with the model that without joining the penalty quadratic term in risky assets using an empirical study of the S&P 500 and several individual stocks in the U.S.
Contents
page Chinese Abstract i Abstract ii Acknowledgement iii Contents iv List of Figures v List of Tables vi
1 Introduction 1
2 Optimization Strategy For Tracking An Index 5 2.1 The Optimization Model.............................................. 5 2.2 The Optimization Control............................................. 8
3 Numerical Results 18
4 Empirical Study 24
5 Conclusion 33
Bibliography 35
A Appendix 37 A.1 Proof of Verification Theorem ....................................... 37
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