作为一个新的研宄范式，行为金融（behavioral finance)最本质的特征是应用心理学的发现去诊察人们的决策制定过程。然而，这些相关应用在投资决策领域，尤其是动态投资组合优化领域，仍然处于初级阶段。期望效用理论框架下的经典投资组合优化模型在数学上对应的是一个容易处理的凸优化_题，而建立在Kahneman and Tversky 前景理论（Prospect Theory, P T ) 基础上的行为投资组合优化模型则常常变成一个非凸的（non-convex)或者时间不一致的(time inconsistent)优化問题。因此，如何恰当地把行为金融领域的新发现应用到实际的资产组合选择中去仍然是个难题。本论文的目标正是想推动这一理论在实践中的应用：我们首先把投资者的心理特征建模到一个标准动态投资组合模型中，然后在由模型推导出来的最优投资策略中找出这些新特征的影响。 / 为了达到这一目标，本论文由探讨投资者行为与投资组合优化的三个独立研宄组成。在第一个研宄中，基于前景理论的S-型价值函数（S-shaped value function)，我们建立了一个多期动态资产组合优化的一般模型。不同于期望效用理论下的经典模型，行为金融理论下的投资组合模型在数学上往往是提法不当的（ill-posed)，常常会得出无穷最优解。He and Zhou [2011]在他们的单期模型中已经非常明确地指出了这一点。因此，我们首先在多期模型框架下找出能限制无穷最优解出现的条件，然后在这些条件之下我们推导出半显式的最优投资策略。特别地，我们发现在两类特殊情形下最优投资策略具有简单的(分片）线性反馈形式。这两类情形分别是：一类是服从任意分布的单个风险资产模型，另一类是服从椭圆分布的多个风险资产模型。也就是说，在这两种情形下分片幂函数型效用函数（S-型价值函数）对应于最优投资策略中的分片线性反馈机制。作为副产品，我们还发现引导出的每一期损失规避测度(induced loss aversion measure)具有时间单调性：它们会随着时间的推移而增大。这种单调性表明一个损失规避型投资者（loss-averse investor)的风险态度在他的整个投资周期里是随着时间变化而变化的。这也进一步为文献中关于投资期限效应（horizon effect)-长期投资者的投资策略是否应该与短期投资者的投资策略不同-这一长期争论的解决提供了线索。 / 在第二个研宄中，我们考察了动态参考水平（dynamic reference p o i n t ) 对于理解、刻画投资者在动态环境下的行为，以及他们的投资模式的作用。基于Arkes et al [2008, 2010]提出的人们看待损失和赢利的不同方式，我们在前景理论的框架下建立了一个参考水平的动态理论模型，并求出了对应的多期投资组合优化模型的半显示解。利用模型推导出来的最优持股股数的U-型属性，我们可以进一步说明人们在对待过去的损失和赢利时表现出来的非对称的自我调整方式与人们在股票交易中表现出来的非对称的交易行为-处置效应(disposition effect)-是有关联的。换句话说，动态参考水平的非对称调整方式在最优策略中表现为非对称的交易行为。我们的实验结果也进一步支持我们提出的理论模型。 / 除了时间维度的变化，我们有理由相信参考水平在空间维度也是不断变换的。作为社会性动物，我们的选择、决策不可避免地会受到身边亲朋好友的影响。我们的第三个研宄正是致力于考察这种社会互动过程。我们考察了PT型投资者与其它市场参与者（比如CRRA型投资者或者其它PT型投资者）的相互影响，以及他们的长期财富水平的收敛性_题。在一个PT型投资者与CRRA型投资者的互动模型中，PT型投资者明确知道CRRA型投资者的最优期末财富水平，并以此作为他的参考水平。如果PT型投资者的初始财富高于CRRA型投资者，那么他只要模仿CRRA型投资者的投资策略就可以保持优势，可以一直做得比CRRA型投资者好。另一方面，如果PT型投资者的初始财富低于CRRA型投资者，那么他只要采取一种“冒险投资策略就可以依然做得比CRRA型投资者好。当交易双方都是PT型投资者时，参考水平的选取可以有两种不同的方式：一种是，两个PT型投资者都以他们的平均财富作为参考水平；另一种是，两个PT型投资者以彼此的财富水平作为自己的参考水平。我们给出了在这两种方式下他们的长期财富得以收敛的充分条件。最后，我们讨论了在给定初始财富水平的情况下，交易双方如何选择最优参考水平的_题。我们从一个简单的博弈模型出发，得到了一个不是很令人满意的结果：在某些情况下均衡不存在。因而，将来我们需要寻找更好的模型去进一步探讨投资者间的这种社会互动与社会影响。 / The most fundamental aspect of the new paradigm of behavioral finance is the relevance of psychological insights in examining decision-making. However, this relevance is still in its early stage in the context of investment decision, especially in the context of dynamic portfolio selection. While the standard preference structure in Expected Utility Theory (EUT) leads to a tractable concave maximization formulation, the new psychological features of Kahneman and Tversky's Prospect Theory (PT), which is frequently applied in behavioral finance, often make related dynamic investment models non-convex and time inconsistent in the sense of optimization, thus intractable in general. Consequently, it is still not easy for us to properly apply insights from behavioral finance in the area of portfolio selection. The goal of this thesis is to translate some remarkable psychological insights associated with P T into investment details by including them in standard dynamic portfolio selection models and then reflecting them in the derived optimal policy. / To achieve this goal, this thesis is composed of three studies on investor behaviors and portfolio models. In the first study, we formulate and investigate a general multi period behavioral portfolio selection model under PT, featuring an S-shaped value function. Unlike the classical expected utility maximization model, a behavioral portfolio model could be easily ill-posed (i.e., infinitely leveraging an asset is optimal for the investor), as He and Zhou [2011] already noticed in their single-period model. Hence, we first discuss the ill-posedness issue and identify the conditions for the well-posedness under a multi-period framework. To be more specific, we show that the well-posedness of a multi-period portfolio selection problem can be characterized in terms of an induced loss aversion measure. Under these well-posedness conditions, we then derive the semi-analytical optimal policy. In particular, for a market of one risky asset or a market of multiple risky assets which follow the elliptical distributions, the optimal behavioral portfolio policy takes a (piecewise) linear feedback form. In other words, the piecewise power utility function (S-shaped value function) is reflected in the derived optimal policy in the form of a piecewise linear feedback policy. As a byproduct, we also find that the induced loss aversion measures for individual time periods tend to increase as the terminal time approaches. This monotonicity property, which implies a changing risk attitude of a loss-averse investor during his investment periods, may shed light on the debate of horizon effect: whether or not a long horizon investor should allocate his wealth differently from a short horizon investor. / In the second study, we investigate the role of dynamic reference point to understand investors' behavior and describe their investment patterns in dynamic situations. In the framework of P T preference, we formulate the dynamics of the reference point by relating it to the way people perceive prior gains and losses, as suggested by Arkes et al [2008, 2010], and then derive a semi-analytical solution for a reference point adapted multi-period portfolio selection model, featuring a piecewise linear utility. Based on an optimal U-shape stock holding property predicted by our model, we further build a linkage between the asymmetric updating rule in reference point adaptation and the asymmetric trading behavior, i.e., the disposition effect. In other words, the asymmetric adaptation of the reference point is reflected in the derived optimal policy in the form of an asymmetric trading pattern. Our experiment also supports the proposed theoretical model. / Besides variation in the time dimension, there are good reasons to believe that the reference point should also change in the spatial dimension. As social animals, our choices and decisions are Inevitably Influenced by our friends and neighbors. In the third study, we address the social interaction process in which PT preferences are influenced by other market participants, e.g., the regular CRRA (Constant Relative Risk Averse) investors or other PT investors, and then study the long run wealth convergence of the two trading parties: one PT agent vs. one CRRA agent or both agents are of PT types. In the one PT agent vs. one CRRA agent model, the PT agent knows the CRRA agent's optimal terminal wealth and takes it as his reference point. If the PT agent also starts with a higher initial wealth level than that of the CRRA agent, he will always do better than the CRRA agent by imitating the CRRA agent's policy. On the other hand, if the PT agent starts with a lower wealth level than that of the CRRA agent, he can still do better than the CRRA agent by adopting a “gambling policy. When both trading parties are PT type investors, we consider two types of reference points: either both PT agents take their average wealth as their reference point or they are mutual reference dependent. Under both situations, we give sufficient conditions on the long run wealth convergence. Finally, we discuss the question: what is the best reference point for both PT agents when their initial wealth levels are given? We start with a simple gamble model and conclude with an unsatisfactory result: no equilibrium pair exists in some situations. Thus, more research efforts are needed in this direction in the future. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Shi, Yun. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves i-vi). / Abstracts also in Chinese. / Abstract --- p.i / Abstract in Chinese --- p.iv / Acknowledgements --- p.vii / Contents --- p.viii / Notations --- p.xii / List of Tables --- p.xvi / List of Figures --- p.xvii / Chapter 1. --- Introduction --- p.1 / Chapter 2. --- Discrete-time Behavioral Portfolio Selection under Prospect Theory --- p.7 / Chapter 2.1. --- Introduction --- p.7 / Chapter 2.2. --- Model Setting --- p.10 / Chapter 2.3. --- Markets with a Single Risky Asset --- p.15 / Chapter 2.4. --- Markets with Multiple Risky Assets following Elliptical Distribution --- p.24 / Chapter 2.5. --- Numerical Study --- p.33 / Chapter 2.6. --- Conclusion --- p.42 / Chapter 2.7. --- Appendices --- p.43 / Chapter 2.7.1. --- Proof of Proposition 2.1 --- p.43 / Chapter 2.7.2. --- Lemmas Used in the Proof of Proposition 2.4 --- p.44 / Chapter 2.7.3. --- Proof of Proposition 2.4 --- p.46 / Chapter 2.7.4. --- Proof of Theorem 2.3 --- p.49 / Chapter 2.7.5. --- Lemma Used in the Proof of Theorem 2.4 --- p.50 / Chapter 2.7.6. --- Proof of Theorem 2.4 --- p.51 / Chapter 3. --- Asymmetric Reference Point Adaptation and its Implication in Deriving the Disposition Effect --- p.56 / Chapter 3.1. --- Introduction --- p.56 / Chapter 3.2. --- Behavioral Portfolio Selection Model with Reference Point Adaptation --- p.61 / Chapter 3.2.1. --- Market Setting --- p.61 / Chapter 3.2.2. --- Self-justification and Positive Reinforcement Reference Point Adaptation --- p.62 / Chapter 3.2.3. --- Multi-period Utility Maximization with Reference Point Adaptation --- p.66 / Chapter 3.2.4. --- Solution to Problem (P) and U-shape Property --- p.68 / Chapter 3.2.5. --- Application: Asymmetric Reference Point Adaptation Drives an Asymmetric Trading Behavior --- p.73 / Chapter 3.3. --- Discussion: Why Asymmetric Adaptation Rule Matters? --- p.80 / Chapter 3.4. --- Experimental Study --- p.83 / Chapter 3.4.1. --- Experiment Method --- p.83 / Chapter 3.4.2. --- Participants --- p.84 / Chapter 3.4.3. --- Design and Procedure --- p.84 / Chapter 3.4.4. --- Hypotheses --- p.86 / Chapter 3.4.5. --- Summary Results --- p.87 / Chapter 3.4.6. --- Test of a Simple Version g(·) --- p.91 / Chapter 3.5. --- Alternative Formulation of Asymmetric Reference Point Adaptation --- p.92 / Chapter 3.5.1. --- Alternative Formulation --- p.92 / Chapter 3.5.2. --- Multi-period Portfolio Selection Model and its Solution --- p.94 / Chapter 3.6. --- Conclusion --- p.99 / Chapter 3.7. --- Appendices --- p.100 / Chapter 3.7.1. --- Proof of Theorem 3.1 --- p.100 / Chapter 3.7.2. --- Proof of Theorem 3.2 --- p.103 / Chapter 3.7.3. --- Instructions to Participants --- p.105 / Chapter 4. --- Interactive Formation of the Reference Point in a Game Model --- p.108 / Chapter 4.1. --- Introduction and Literature --- p.108 / Chapter 4.2. --- CRRA Agent vs. PT Agent --- p.112 / Chapter 4.2.1. --- Theoretical Model --- p.112 / Chapter 4.2.2. --- Toy Example-1: One-step Success? --- p.114 / Chapter 4.3. --- PT-1 Agent vs. PT-2 Agent --- p.118 / Chapter 4.3.1. --- Average Wealth as Reference Point --- p.118 / Chapter 4.3.2. --- Toy Example-2: Converge or Diverge? --- p.120 / Chapter 4.3.3. --- Mutual Reference Dependence --- p.122 / Chapter 4.3.4. --- Toy Example-3: Converge or Diverge? --- p.123 / Chapter 4.4. --- Optimal Reference Point Selection --- p.125 / Chapter 4.4.1. --- Situation 1: Both PTs with Aggressive Targets --- p.127 / Chapter 4.4.2. --- Situation 2: PT-1 Agent with Conservative Target, PT-2 Agent with Aggressive Target --- p.130 / Chapter 4.5. --- Conclusion and Future Work --- p.133 / Chapter 4.6. --- Appendices --- p.136 / Chapter 4.6.1. --- Proof of Theorem 4.5 --- p.136 / Chapter 4.6.2. --- Proof of Theorem 4.6 --- p.137 / Chapter 4.6.3. --- Proof of Theorem 4.7 --- p.138 / Chapter 4.6.4. --- Proof of Theorem 4.8 --- p.141 / Chapter 5. --- Conclusion --- p.144 / Bibliography --- p.i
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_328414 |
| Date | January 2013 |
| Contributors | Shi, Yun, Chinese University of Hong Kong Graduate School. Division of Systems Engineering and Engineering Management. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | electronic resource, electronic resource, remote, 1 online resource (xviii, 146, vi leaves) : ill. (some col.) |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
Page generated in 0.0308 seconds