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系統識別號 U0026-0812200913453257
論文名稱(中文) 穩定分配在最佳化投資組合選擇的應用
論文名稱(英文) Stable Distribution with Application on Optimal Portfolio Selection
校院名稱 成功大學
系所名稱(中) 統計學系碩博士班
系所名稱(英) Department of Statistics
學年度 95
學期 2
出版年 96
研究生(中文) 白明欣
研究生(英文) Ming-Hsin Pai
電子信箱 r2694117@mail.ncku.edu.tw
學號 r2694117
學位類別 碩士
語文別 英文
論文頁數 38頁
口試委員 口試委員-蘇永在
口試委員-梁雪富
指導教授-黃銘欽
中文關鍵字 穩定分配  最佳投資組合選擇  效用函數 
英文關鍵字 optimal portfolio selection  utility function  stable distribution 
學科別分類
中文摘要 投資組合是廣泛被用在分散風險的財務工具。本論文研究投資組合在穩定分配模型以及常態分配模型假設下的報酬表現。本研究指出假設為穩定分配模型的投資組合會比假設為常態分配的投資組合,在相同的風險水準之下具有較高的夏普指數。本研究同時探討了包含了無風險資產的投資組合。
英文摘要 Portfolios are widely-used tool to diversify the risk. This thesis studied portfolio performances under sub-Gaussian stable distribution models and normal distribution models. The study indicated that the portfolios constructed by stable distribution gave higher Sharpe ratio than normal distribution under the same risk level. The thesis also explored the inclusion of riskless asset in the portfolio.
論文目次 Chapter 1 Introduction…………………………………………………………1
1.1 Motivation and objective…………………………………………1
1.2 Structure………………………………………………………2
Chapter 2 Literature Review………………………………………………3
2.1 Portfolio theory ………………………………………………3
2.2 Stable distribution ………………………………………………………5
Chapter 3 Model Specification and Methodology………………………7
3.1 Properties of stable distributions……………………………………7
3.2 Appropriateness of stable distribution model…………………12
3.3 Stable model with portfolio theory……………………………13
3.3.1 Markowitz portfolio theory………………………………13
3.3.2 Sub-Gaussian stable distribution in portfolio……………15
3.3.3 Utility function……………………………………………18
Chapter 4 Empirical Results………………………………………20
4.1 Data adaptability………………………………………………20
4.2 Comparing stable and normal models…………………………24
4.3 Empirical results of bearish market……………………………28
Chapter 5 Conclusions…………………………………………31
5.1 Conclusions………………………………………………………31
References ……………………………………………………………32
Appendix Ⅰ……………………………………………………………34
Appendix Ⅱ……………………………………………………………36
Appendix Ⅲ……………………………………………………………37
Appendix Ⅳ……………………………………………………………38
參考文獻 1. Belkacem, L., J. L. Véhel, and C. Walter, “CAPM, Risk and Portfolio Selection in “Stable Markets”” Rapport de recherché de l'INRIA – Rocquencourt, Janvier 1996.
2. Doganoglu, T., S. Mittnik and S. Rachev, “Portfolio selection in the presence of heavy-tailed Asset Return”, Contribution to Modern Econometric: From Data Analysis to Economic Policy, Springer, 2002.
3. Fisher, L. and J. H. Lorie, “Some Studies of Variability of Returns on Investment in Common Stocks” The Journal of Business, Vol.43, No.2, P.99-134, April, 1970.
4. Li, D. and W. L. Ng, “Optimal Dynamic portfolio selection Multiperiod Mean-Variance formulation”, Mathematical Finance, Vol.10, Issue.3, p.387-406, 2000.
5. Mandelbrot, B. B. “The Variance of Certain Speculative Prices.” Journal of Business Vol.36, p.394-419, 1963.
6. Nolan, J. P., A. K. Panorska and J. H. McCulloch, “Estimation of stable spectral measures”, Mathematical and Computer Modelling, Volume 34, Issues 9-11, p.1113-1122, November 2001.
7. Ojeda, D., “Comparison of stable estimators”, Ph.D. Thesis, Department of Mathematics and statistics, American University, 2001.
8. Ortobelli, S., I. Huber and E. Schwartz, “Portfolio selection with stable distribution returns”, Mathematical Methods of Operations Research, Volume 55, No.2, p.265-300, 2002.
9. Rachev, S. and S. Han, “Portfolio management with stable distributions”, Mathematical Methods of Operations Research, Volume 51, p.341-352, 2000.
10. Rachev, S. T. “Handbook of Heavy Tailed Distributions in Finance”, Elsevier, 2003.
11. Rachev, S.T., C. Menn, and F. J. Fabozzi, “Fat-Tailed and Skewed Asset Return Distribution,” John Wiley & Sons, 2005.
12. Rachev, S. T., S. Stoyanov, A. Biglova and F. J. Fabozzi, “An Empirical Examination of Daily Stock Return Distributions for U.S. Stocks”, Data Analysis and Decision Support, Springer Series in Studies in Classification, p.269-281, 2005.
13. Rachev, S. T., S.V. Stoyanov, C. F. Wu and F. J. Fabozzi, “Empirical Analyses of Industry Stock Index Return Distribution for the Taiwan Stock Exchange” Annals of Economics and Finance, Vol.8, No.1, p.21-31, 2007.
14. Samorodnitsky, G. and M. S. Taqqu, “Stable Non-Gaussian Random Processes” Chapman & Hall, 1994.
15. Sharpe, W. F., “The Sharpe ratio”, Journal of Portfolio Management, Vol.21, Issue 1, p.49-58, 1994.
16. Zolotarev, V. M. “One-dimensional Stable Distribution”, American Mathematical Society, 1986.
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