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題名：最適動態資產配置暨理性預期均衡
作者：黃鴻禧 引用關係
作者(外文)：Huang, Hung-Hsi
校院名稱：國立臺灣大學
系所名稱：財務金融學研究所
指導教授：周國端
學位類別：博士
出版日期：2002
主題關鍵詞：投資組合；資產配置；資訊不對稱；理性預期均衡；兩項基金分離；動態資產配置；動態投資組合前緣；隨機動態規劃；Portfolio；Asset Allocation；Information Asymmetry；Rational Expectations Equilibrium；Two Funds Separation；Dynamic Asset Allocation；Dynamic Portfolio Frontier；Stochastic Dynamic Programming
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本論文總共有三篇文章，分別探討關於投資組合理論的三個議題，我們以嚴謹數理推演方式，導出各議題的重要結論，茲將論文內容及研究成果摘要如下。
第一篇：理性預期均衡之訊息揭露
本文旨在探討當市場交易者有差別私有訊息時，證券市場之均衡性質，達到兩項基金分離的條件，以及闡釋均衡價格的揭露訊息功能。在風險性資產與私有訊息服從多元常態分配之假設下，我們推導出各種均衡的資產均衡價格，並且證明以精度為權數的加權平均訊息，不但是未來資產報酬之充分統計量，也是最佳估計量。除此之外，本文說明了市場競爭均衡並非理性預期均衡，且說明了理性預期均衡可以升格為充分訊息均衡之條件，又當理性預期均衡可以升格為充分訊息均衡時，則此時之交易價格可以充分揭露訊息。
第二篇：考慮交易成本之多期動態投資決策
本文旨在闡示當有實際交易成本時，如何極大化預期最終財富效用的動態投資決策問題。此重要的問題至今尚無完整解答，我們所提出之數值聯立解法，首創求出此類問題之通解。除此之外，只要是多期動態投資決策問題，不論效用函數的型式及資產報酬率的原始分配為何，我們所提供之聯立解法，再搭配多重格子法，皆可求出數值解。最後，本文以股票資產及銀行存款資產為例，先作資產報酬率的預測，再透過本文所提供的聯立解法，撰寫電腦程式，求出最適的動態投資決策。
第三篇：動態資產配置下的投資組合前緣
過去學者須運用Martingale理論及假設完全市場，始可導出動態組合前緣理論，而且必須當資產報酬率服從某特定機率分配，才可得出動態組合前緣的顯明解。由於完全市場的假設與實際不相符合，而且Martingale理論並不適合於個人投資選擇問題上。故本文乃放鬆完全市場假設及不採用Martingale理論，並不限定資產報酬率的機率分配，導出動態資產配置下的投資組合前緣理論。我們利用嚴謹的數學推導，求出動態投資組合前緣的顯明解及對應的動態資產配置。最後，本文利用電腦模擬方式，繪出動態投資組合前緣與靜態投資前緣，圖形強烈顯示動態投資組合前緣較有效率。
This dissertation contains three essays about the portfolio theory. We mathematically derive various theorems in each essay. The contents and the main results of each essay are summarily displayed as follows.
Essay 1: The Information Revealing for Rational Expectations Equilibrium
This article presents the property of security market equilibrium, the condition of two funds separation, and the revealing information of equilibrium prices. We assume that the traders in security market have differential information about asset value. Moreover, we assume that rates of return on risky assets and private information of traders are multivariate normally distributed. Under these assumptions, we derive equilibrium prices of risky assets and obtain some important results as follows. First, we prove that average information weighted by precision is sufficient statistic as well as maximum likelihood estimator about future asset return. Second, we show that market competitive equilibrium is not rational expectations equilibrium. Third, we derive the condition that rational expectations equilibrium can elevate to full information equilibrium. While rational expectations equilibrium can elevate to full information equilibrium, trading prices can fully reveal information.
Essay 2: Multiperiod Dynamic Investment Strategies with Transaction Costs
This article presents the dynamic investment problem that investor maximizes his expected utility of terminal wealth in the presence of realistic transaction costs. This important problem has not been solved completely since today. We first develop a new numerical approach to solve it. Furthermore, our numerical approach combined with multi-grid method can completely solve all the multiperiod dynamic investment problems regardless of the investor’s utility function and the distributions of asset returns. Finally, we examine an example of two assets that consist of one stock asset and one bank deposit. We predict their return distributions and then derive the optimal dynamic investment strategies by using our numerical approach combined with computer programs.
Essay 3: The Portfolio Frontier under Dynamic Asset Allocation
Although previous scholars have derived the theory of dynamic portfolio frontier, they must constrain some conditions. These constraints include martingale approach, the assumption of complete market, and particular probability distribution of asset returns. Since the complete market does not exist in the real world and the martingale approach cannot apply to individual investment, we relax these constraints. Even though this paper relaxes these constraints, we can also derive the explicit solution of dynamic portfolio frontier as well as corresponding dynamic asset allocation. Finally, we draw the dynamic portfolio frontier and static portfolio frontier by computer simulation. These graphs obviously display that the dynamic portfolio frontier is more efficient.
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