以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：197

、訪客IP：3.147.13.185

姓名	陳宇畋(Yeu-Tian Chen)  查詢紙本館藏	畢業系所	光機電工程研究所
論文名稱	財經系統與控制: 資本資產定價模型的明確最佳化 (Financial System and Control: Exact Optimization for Capital Asset Pricing Model)
相關論文	★ 使用快速狀態相關微分Riccati方程方案的衝擊角導引 ★ 永磁同步馬達的實時硬體控制平台，使用基於觀測器之SDRE控制策略 ★ 使用快速觀測器的SDRE控制方案應用在電動車的馬達驅動系統 ★ 使用狀態相關Riccati方程式控制器設計實現雙輪機器人 ★ 基於快速狀態相關微分形式黎卡迪方程式導控策略對於機動目標的攔截於預先規畫之方向
檔案	[Endnote RIS 格式]    [Bibtex 格式]    [相關文章]   [文章引用]   [完整記錄]   [館藏目錄]   至系統瀏覽論文 ( 永不開放)
摘要(中)	優化在當今世界無處不在。特別是，金融領域觀察到了控制和優化之間的明確聯繫，這些聯繫受投資動態框架的制約。更深入地說，二次規劃（quadratic programming, QP，優化的基礎）和黎卡迪方程（Riccati equation，最優控制的基礎）之間的關係可以通過封閉形式的方程來解釋，據作者所知，這種解釋僅出現在金融系統和控制的應用中。本論文使用了基於明確最佳化之求解方法應用於計算資本資產定價模型(Capital asset pricing model, CAPM)。參考之模型為零變異數CAPM，其透過零變異數投資組合解放對於無風險利率的假設。相較於主流文獻採用數值方法來完成，本文採用之等式限制二次規劃的明確解，此方法接近零變異數CAPM的設計精神，從而讓我們從效率前緣中選取最佳市場投資組合。除此之外，此方法對應於半正定的共變異數矩陣的解析解，這也符合馬可維茲對於投資多元化之設想。我們的研究成果有助於拓展金融經濟學的經典問題。最後，根據實證驗證，本研究結果初步的展示了對於金融市場實際情況的適用性，更進一步提高了人們對此方法的興趣。
摘要(英)	Optimization is ubiquitous in the world today. In particular, the field of finance observes the explicit connection between control and optimization, which is subject to the framework of investment dynamics. To be more in-depth, the relation between quadratic programming (QP, a basis in optimization) and Riccati equation (a basis in optimal control) can be interpreted in terms of closed-form equations, which, to the best of author′s understanding, only appears in the application to financial systems and control. This paper employs an optimization-based method grounded in precision to apply to the Capital Asset Pricing Model (CAPM) in an application-oriented manner. The model referenced in this study is the Zero-Variance CAPM, which, through zero-variance portfolios, liberates itself from the assumption of a risk-free rate. In contrast to prevalent literature utilizing numerical methods, this paper adopts an equality-constrained QP approach. This method allows us to select market portfolios from the efficient frontier, bringing us closer to the theoretical thought process initially envisaged. Moreover, the methodology used corresponds to an analytical solution for the semi-positive definite covariance matrix, aligning with Markowitz′s conception of investment diversification. Consequently, the results may contribute to extending classical problems in financial economics. Finally, empirical validation suggests preliminary applicability to real-world financial market conditions, further augmenting interest in this approach.
關鍵字(中)	★ 投資組合選擇 ★ 效率前緣 ★ 資本資產定價模型 ★ 明確最佳化 ★ 二次規劃	關鍵字(英)	★ Portfolio Selection ★ Efficient Portfolio Frontier ★ Capital Asset Pricing Model ★ Exact Optimization ★ Quadratic Programming
論文目次	摘要 i Abstract ii 誌謝 iv 目錄 vi 圖目錄 viii 縮寫列表 ix 符號說明 x 一、緒論 1 1.1 研究動機 1 1.2 本文結構 4 二、文獻回顧 5 三、問題描述 7 3.1 術語與常用縮寫 7 3.2 等式約束二次規劃 8 3.3 投資組合選擇 10 3.4 資本資產定價模型(CAPM) 12 四、實證研究 15 4.1 數據獲取及取樣方式說明 15 4.2 實證之結果與分析 16 五、結論與未來展望 22 5.1 結論 22 5.2 未來展望 23 參考文獻 25 附錄A 文獻回顧 33
參考文獻	[1] R. C. Merton, “An analytic derivation of the efficient portfolio frontier,” J. Financ. Quant. Anal., vol. 7, no. 4, pp. 1851–1872, 1972. [2] D. G. Luenberger and Y. Ye, Linear and Nonlinear Programming, 5th ed. Springer, Switzerland, 2021, and its 2nd ed. (2003). [3] H. Markowitz, “Portfolio selection,” J. Financ., vol. 7, no. 1, pp. 77–91, 1952. [4] W. F. Sharpe, “Capital asset prices: A theory of market equilibrium under conditions of risk,” J. Financ., vol. 19, no. 3, pp. 425–442, 1964. [5] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge University Press, Cambridge, UK, 2004, 27th/latest printing with corrections, 2021, and its solution manual. [6] W. S. Dorn, “Non-linear programming–A survey,” Manage. Sci., vol. 9, no. 2, pp. 171–208, 1963. [7] Y. Nesterov, Lectures on Convex Optimization, 2nd ed. Springer, Cham, Switzerland, 2018, vol. 137. [8] A. S. Nemirovsky and D. B. Yudin, Problem Complexity and Method Efficiency in Optimization. A Wiley-Interscience Publication, John Wiley & Sons Inc., New York, 1983, translated from the Russian and with a preface by E.R. Dawson, Wiley-Interscience Series in Discrete Mathematics. [9] J. Nocedal and S. J. Wright, in Numerical Optimization, second/latest ed., ser. Springer Series in Operations Research and Financial Engineering, T. V. Mikosch, S. I. Resnick, and S. M. Robinson, Eds. Springer, USA, 2006. [10] L.-G. Lin and Y.-W. Liang, “Exact Optimization: Part I,” Taiwan. J. Math., vol. 27, no. 1, pp. 169–205, 2023. [11] L.-G. Lin, Y.-W. Liang, and W.-Y. Hsieh, “Convex quadratic equation,” J. Optim. Theory Appl., vol. 186, no. 3, pp. 1006–1028, 2020. [12] Y. Qi, “Classifying the minimum-variance surface of multiple-objective portfolio selection for capital asset pricing models,” Ann. Oper. Res., vol. 311, no. 2, pp. 1203–1227, 2022. [13] D. D. Wackerly, W. Mendenhall III, and R. L. Scheaffer, Mathematical Statistics with Applications, 7th ed. Cengage Learning, Canada, 2008. [14] W. F. Sharpe, “A simplified model for portfolio analysis,” Manage. Sci., vol. 9, no. 2, pp. 277–293, 1963. [15] O. Ledoit and M. Wolf, “Improved estimation of the covariance matrix of stock returns with an application to portfolio selection,” J. Empir. Financ., vol. 10, no. 5, pp. 603–621, 2003. [16] P. N. Kolm, R. Tütüncü, and F. J. Fabozzi, “60 years of portfolio optimization: Practical challenges and current trends,” Eur. J. Oper. Res., vol. 234, no. 2, pp. 356–371, 2014. [17] A. Gunjan and S. Bhattacharyya, “A brief review of portfolio optimization techniques,” Artif. Intell. Rev., vol. 56, pp. 3847–3886, 2023. [18] M. Rubinstein, “Markowitz’s “Portfolio Selection”: A fifty-year retrospective,” J. Financ., vol. 57, no. 3, pp. 1041–1045, 2002. [19] Y. Qi, K. Liao, T. Liu, and Y. Zhang, “Originating multiple-objective portfolio selection by counter-COVID measures and analytically instigating robust optimization by mean-parameterized nondominated paths,” Oper. Res. Perspect., vol. 9, p. 100252, 2022. [20] T. Bodnar, N. Parolya, and W. Schmid, “On the equivalence of quadratic optimization problems commonly used in portfolio theory,” Eur. J. Oper. Res., vol. 229, no. 3, pp. 637–644, 2013. [21] J. Tu and G. Zhou, “Markowitz meets talmud: A combination of sophisticated and naive diversification strategies,” J. Financ. Econ., vol. 99, no. 1, pp. 204–215, 2011. [22] O. Ledoit and M. Wolf, “Nonlinear shrinkage of the covariance matrix for portfolio selection: Markowitz meets goldilocks,” The Rev. Financ. Stud., vol. 30, no. 12, pp. 4349–4388, 2017. [23] E. J. Elton, M. J. Gruber, and M. W. Padberg, “Simple criteria for optimal portfolio selection,” J. Financ., vol. 31, no. 5, pp. 1341–1357, 1976. [24] W. Xu, X. Chen, and T. F. Coleman, “The efficient application of automatic differentiation for computing gradients in financial applications,” J. Comput. Financ., vol. 19, no. 3, pp. 71–96, 2016. [25] N. Gârleanu and L. H. Pedersen, “Dynamic trading with predictable returns and transaction costs,” J. Financ., vol. 68, no. 6, pp. 2309–2340, 2013. [26] Y. Qi and R. E. Steuer, “On the analytical derivation of efficient sets in quad-and-higher criterion portfolio selection,” Ann. Oper. Res., vol. 293, pp. 521–538, 2020. [27] Y. Qi and X. Li, “On imposing ESG constraints of portfolio selection for sustainable investment and comparing the efficient frontiers in the weight space,” SAGE Open, vol. 10, no. 4, p. 2158244020975070, 2020. [28] X. Deng and C. Huang, “Some new results in theory and application on positive definiteness of portfolio covariance matrix,” IAENG Int. J. Appl. Math., vol. 51, no. 1, pp. 1–6, 2021. [29] V. Guigues, “Sensitivity analysis and calibration of the covariance matrix for stable portfolio selection,” Comput. Optim. Appl., vol. 48, no. 3, pp. 553–579, 2011. [30] C. C. Y. Kwan, “What really happens if the positive definiteness requirement on the covariance matrix of returns is relaxed in efficient portfolio selection?” Financ. Mark. Portfolio Manag., vol. 32, pp. 77–110, 2018. [31] R. Roll, “A critique of the asset pricing theory’s tests part I: On past and potential testability of the theory,” J. Financ. Econ., vol. 4, no. 2, pp. 129– 176, 1977. [32] J. Malick, “A dual approach to semidefinite least-squares problems,” SIAM J. Matrix Anal. Appl., vol. 26, no. 1, pp. 272–284, 2004. [33] T. Bodnar, S. Mazur, and H. Nguyen, “Estimation of optimal portfolio compositions for small sample and singular covariance matrix,” Örebro University, School of Business, Working Papers 2022:15, 2022. [34] M. Gulliksson, A. Oleynik, and S. Mazur, “Portfolio selection with a rankdeficient covariance matrix,” Comput. Econ., 2023. [35] Z. Zhao, O. Ledoit, and H. Jiang, “Risk reduction and efficiency increase in large portfolios: Gross-exposure constraints and shrinkage of the covariance matrix,” J. Financ. Econom., vol. 21, no. 1, pp. 73–105, 2023. [36] A. L. Lewis, “A simple algorithm for the portfolio selection problem,” J. Financ., vol. 43, no. 1, pp. 71–82, 1988. [37] P. Barroso and K. Saxena, “Lest we forget: Learn from out-of-sample forecast errors when optimizing portfolios,” The Rev. Financ. Stud., vol. 35, no. 3, pp. 1222–1278, 2022. [38] Y. Qi, R. E. Steuer, and M. Wimmer, “An analytical derivation of the efficient surface in portfolio selection with three criteria,” Ann. Oper. Res., vol. 251, pp. 161–177, 2017. [39] M. B. Haugh and A. W. Lo, “Computational challenges in portfolio management,” Comput. Sci. Eng., vol. 3, no. 3, pp. 54–59, 2001, in the special issue of “Tomorrow’s Hardest Problems”. [40] T. Bodnar, N. Parolya, and W. Schmid, “On the exact solution of the multiperiod portfolio choice problem for an exponential utility under return predictability,” Eur. J. Oper. Res., vol. 246, no. 2, pp. 528–542, 2015. [41] C. DeBacco. (2023) Post-modern portfolio theory (latest version, summer 2020). Summer Scholarship, Creative Arts and Research Projects (SCARP). 8. [Online]. Available: https://jayscholar.etown.edu/scarp/8 [42] F. Furini, E. Traversi, P. Belotti, A. Frangioni, A. Gleixner, N. Gould, L. Liberti, A. Lodi, R. Misener, H. Mittelmann, N. V. Sahinidis, S. Vigerske, and A. Wiegele, “QPLIB a library of quadratic programming instances,” Math. Prog. Comp., vol. 11, pp. 237–265, 2019. [43] H. Markowitz, Portfolio Selection: Efficient Diversification of Investments, 2nd ed. Yale University Press, USA, 1959. [44] Z. Bodie, A. Kane, and A. J. Marcus, Investments, 5th ed. McGraw-Hill Book Company, USA, 2002. [45] F. Black, “Capital market equilibrium with restricted borrowing,” J. Bus., vol. 45, no. 3, pp. 444–455, 1972. [46] E. F. Fama, Foundations of finance: Portfolio decisions and securities prices, 1st ed. Basic Books, New York, NY, 1976. [47] R. A. Brealey, S. C. Myers, and F. Allen, Principles of Corporate Finance, 10th ed. McGraw-hill, 2010. [48] J. L. G. Board, C. M. S. Sutcliffe, and W. T. Ziemba, Portfolio Theory: Mean-Variance Model. Boston, MA: Springer US, 2013, pp. 1142–1148. [49] P. J. Ryan and J. Lefoll, “A comment on mean-variance portfolio selection with either a singular or a non-singular variance-covariance matrix,” Journal of Financial and Quantitative Analysis, vol. 16, no. 3, pp. 389– 395, 1981. [50] B. Stellato, G. Banjac, P. Goulart, A. Bemporad, and S. Boyd, “OSQP: An operator splitting solver for quadratic programs,” Math. Program. Comput., vol. 12, no. 4, pp. 637–672, 2020. [51] S. K. Vadlamani, T. P. Xiao, and E. Yablonovitch, “Physics successfully implements Lagrange multiplier optimization,” Proc. Natl. Acad. Sci., vol. 117, no. 43, pp. 26 639–26 650, 2020.
指導教授	林立岡(Li-Gang Lin)	審核日期	2024-7-31
推文	facebook   plurk   twitter   funp   google   live   udn   HD   myshare   reddit   netvibes   friend   youpush   delicious   baidu
網路書籤	Google bookmarks   del.icio.us   hemidemi   myshare