在非確定環境下最優投資組合策略

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秦承偉(Chengwei Qin) 查詢紙本館藏

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統計研究所

論文名稱

在非確定環境下最優投資組合策略
(Optimal Portfolio Strategies Under the Environment with Uncertainties)

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摘要(中)

投資者通常無法准確地把握投資期限，因為投資大多時候會因為
某些意想不到的事情而終止，例如投資代理死亡。但有時他們會知道
一些與投資期限相關的信息，並由此來決定投資策略。在這篇文章中，
我們把重點放在分析和討論股票收益率預測性、模型參數不確定性和
投資期限不確定性等因素對於投資策略的影響上。這個研究包含了兩
個不同的投資方式。首先，我們通過一個離散的資產分配模型提出了
買入持有策略，即在投資結束前不會改變資產分配權重；另一方面，
對於資產分配權重隨着時間變動的動態模型，我們將用到連續時間模
型。我們嘗試找出二者的最佳投資策略，從而使得在投資結束時所獲
得的總收益達到最大。

摘要(英)

Mostly, investors fail to accurately determine the length of the investment horizon. In
many cases, the investment will stop because of some unexpected accidents such as the
death of the agent. But sometimes they may have other informations related to the length
of horizon which can give them an access to optimize their portfolio strategies. In this
paper, we concentrate on investigating how will the portfolio strategies be eected by the
stochastic time-horizon and other two uncertainties including returns predictability and
parameter uncertainty. Our research will involve two dierent investment philosophies.
Firstly, we analyse the buy-and-hold strategy by a discrete-time model so that the portfolio
choice can be static until the investment gets nished. On the other hand, we propose the
continuous-process when considering the allocation weights are dynamic which means the
strategies will be changed over time. Our primary purposes for both of them are trying
to nd the optimal strategies which can maximize the wealth in terminal time.

關鍵字(中)

★ 不確定性
★ 最佳投資策略
★ 預測性回歸
★ HJB方程
★ 貝氏分析
★ VAR模型

關鍵字(英)

★ Uncertainties
★ Optimal portfolio strategy
★ Predictive regressions
★ HJB equations
★ Bayesian analysis
★ VAR model

論文目次

1 Introduction 1
2 The Buy-and-Hold Portfolio Strategy 4
2.1 The portfolio strategy for a buy-and-hold investor . . . . . . . . . . . . . . 4
2.2 The data description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3 Asset Allocation Analysis When Returns Are Independent 15
3.1 The predictive distribution for i.i.d stock returns . . . . . . . . . . . . . . . 15
3.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2.1 When parameters are certain . . . . . . . . . . . . . . . . . . . . . 18
3.2.2 When parameters are uncertain . . . . . . . . . . . . . . . . . . . . 21
4 Asset Allocation Analysis Under Predictive Regressions 25
4.1 Constructing the predictive distribution under predictive regressions . . . . 25
4.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2.1 When parameters are certain . . . . . . . . . . . . . . . . . . . . . 27
4.2.2 When parameters are uncertain . . . . . . . . . . . . . . . . . . . . 31
5 From A Perspective Of Dynamic Asset Allocation 35
5.1 Dynamic asset allocation regardless the predictor . . . . . . . . . . . . . . 35
5.1.1 Solution when A = 1 . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.1.2 Solution when 0 < A < 1 . . . . . . . . . . . . . . . . . . . . . . . . 39
i
5.2 Dynamic asset allocation with predictor . . . . . . . . . . . . . . . . . . . 40
6 Conclusion 45
Reference 48

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指導教授

傅承德(Cheng-Der Fuh)

審核日期

2013-7-2

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