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研究生:羅盛豐
研究生(外文):Sheng-Feng Luo
論文名稱:隨機持有期間下之投資組合選擇問題與其財務應用
論文名稱(外文):Portfolio Selection, Random Horizon, and Financial Applications
指導教授:傅承德傅承德引用關係
指導教授(外文):Cheng-Der Fuh
口試委員:許順吉廖四郎張傳章石百達
口試委員(外文):Shuenn-Jyi SheuSzu-Lang LiaoChuang-Chang ChangPai-Ta Shih
口試日期:2013-06-10
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:財務金融學研究所
學門:商業及管理學門
學類:財務金融學類
論文種類:學術論文
論文出版年:2013
畢業學年度:101
語文別:英文
論文頁數:82
中文關鍵詞:投資組合選擇隨機持有期間夏普比率出場時間之不確定性風險財務傳染效果多維更新理論
外文關鍵詞:Portfolio SelectionRandom HorizonSharpe RatioTime Uncertainty RiskContagion EffectMultivariate Renewal Theory
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本論文在考慮投資人出場時間不確定之下,研究一個相當於馬可維茲投資組合理論的最適選擇問題。其中,我們訂定一個停止門檻之規則去描述投資人何時會選擇離開投資市場。在此設定下,我們可以利用一個多維更新理論去近似收益率的機率分佈,進而提供可成功刻劃最適解之解析逼近。利用所得到的最適投資權重之逼近公式,我們進一步研究不確定出場時間下的最佳投資組合如何偏離原馬可維茲的最適解,並指出何時此二選擇會相同。其中,我們特別注意到,當市場遵循資本資產訂價模式且停止門檻恰好設立在市場投資組合之上時,這兩個投資組合選擇理論會產生相同的切點投資組合。此外,我們還試著用一種時段選擇調整過後的夏普比率去比較這兩個來自不同理論之投資組合的績效表現和效率。最後,相對於傳統馬可維茲的投資人來說,雖然我們的投資者面對著額外的出場時間不確定性之風險,我們發現他們的最佳投資選擇並不一定會全然降低對純風險資產的需求。

This thesis studies a Markowitz equivalent portfolio selection problem with random horizon, to which the horizon is specified by a threshold stopping rule describing when to exit the market. Under this setting, we can approximate the
stopped return distributions via a multivariate renewal theory, and then provide an analytical approximation that successfully characterizes the optimal solution. By using the obtained analytic formulas, we further study how the current optimal portfolio weights deviate from the classical Markowitz’s solution, and also indicate when they are the same. In particular, we note that these two settings generate the same tangency portfolio when CAPM holds and the stopping rule is defined on the market portfolio. In addition, we also try to compare the performance and
efficiency of these two portfolios based on a timing-adjusted Sharpe ratio. Finally, relative to Markowitz’s investor, we find that our investor, facing such additional
time uncertainty risk, does not necessarily reduce his/her optimal demand for risky assets.

口試委員會審定書 i
誌謝 ii
中文摘要 iii
Abstract iv
1 Introduction 1
2 Problem Formulation 7
2.1 Static Portfolio Selection . . . . . . . . . . . . 7
2.2 Independent Exit . . . . . . . . . . . . . . . . . 9
2.3 Dependent Exit . . . . . . . . . . . . . . . . . . 11
3 Analytical Approximation 13
3.1 Optimal Portfolio Under Random Horizon . . . . . . 13
3.2 Comparison with Markowitz Solution . . . . . . . . 17
3.3 Time Uncertainty Risk . . . . . . . . . . . . . . . 25
4 Numerical Analysis 29
4.1 Monte Carlo Simulation . . . . . . . . . . . . . . 29
4.2 Approximation Performance . . . . . . . . . . . . . 34
4.3 Check Asymptotic Properties for Exact Solutions . . 35
5 Model Applicability 41
5.1 Equity Premium Puzzle . . . . . . . . . . . . . . . 41
5.2 Contagion Effect . . . . . . . . . . . . . . . . . 42
5.3 Safety-First Constraint . . . . . . . . . . . . . . 44
6 Concluding Remarks 47
Appendix 51
A Proofs of Theorem 1 & Other Associated Results . . . 51
B Proofs of Theorem 2 & Its Corollaries . . . . . . . . 63
C Proofs of Propositions 1 & 2 . . . . . . . . . . . . 69
D A Dynamic Portfolio Selection Problem . . . . . . . . 72
Bibliography 79

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