隨機持有期間下之投資組合選擇問題與其財務應用

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。

關鍵字

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

並列摘要

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.

並列關鍵字

Portfolio Selection ； Random Horizon ； Sharpe Ratio ； Time Uncertainty Risk ； Contagion Effect ； Multivariate Renewal Theory

參考文獻

01. Allen, F. and D. Gale (2000). Financial contagion, Journal of Political Economy 108, 1–33.

02. Baur, D. G. and B. M. Lucey (2009). Flights and contagion—An empirical analysis of stock-bond correlations, Journal of Financial Stability 5, 339–352.

03. Blanchet-Scalliet, C., N. El Karoui, M. Jeanblanc, and L. Martellini (2008). Optimal investment decisions when time-horizon is uncertain, Journal of Mathematical Economics 44, 1100–1113.

04. Bouchard, b. and H. Pham (2004).Wealth-path dependent utility maximization in incomplete markets, Finance and Stochastics 8, 579–603.

07. Davies, J. B. (1981). Uncertain lifetime, consumption and dissaving in retirement, Journal of Political Economy 89, 561–577.

國際替代計量

隨機持有期間下之投資組合選擇問題與其財務應用

全文下載

主題瀏覽