信息优势与投资组合优化

发布时间：2018-04-01 20:22

本文选题：信息　切入点：HJB方程　出处：《清华大学》2014年硕士论文

【摘要】：借助于Ito发展出随机分析理论，数理金融学进入了一个新时代，大量的刻画金融市场的随机模型被开发出来，并且基于相应的金融市场模型的衍生品定价问题，投资组合优化问题也逐一得到解决。不同于重点关注对市场结构进行刻画的研究思路，行为金融学理论关注市场参与者本身的差异性，并注意到了信息不对称对投资者决策的影响，但是信息差异很难用数学模型刻画，以至相关的研究主要集中于描述性的分析。不同常见的描述性分析，本文尝试了对某一类信息差异进行数学刻画，在一个带状态转换的市场模型下解决了拥有不同信息的投资者在给定信息时的投资组合优化问题。为了让读者迅速了解我们的重要思想，本文首先借助一个游戏说明了信息如何影响人的决策行为。在这个游戏中，不同的玩家知道的信息不同，直接导致他们在相同的游戏目标之下，使用的策略完全不同。然后我们把注意力转移到我们真正的研究对象—资本市场，我们首先根据真实市场的情况建立了一个市场模型，在这个市场模型下，有无风险债券，周期性行业股票，，和非周期性行业股票，接着我们用数学方式描述了几类不同的与真实市场投资者相对应的典型投资者，不同的投资者之间的差距在于他们对于能对市场有重大影响的信息的获取能力和处理能力不同，从而他们在做出投资决策时所拥有的信息是不相同的。我们利用HJB方程方法给出了不同投资者在给定各自信息的条件下的均值方差（Mean Variance）有效策略以及相应的有效边界，并且揭示了条件均值方差有效策略和无条件均值方差有效策略之间的重要联系。我们发现一个投资者的无条件均值方差有效策略必须是给定该投资者所掌握信息的条件下的均值方差有效策略，但是并不是一个任意一个条件均值方差有效策略都一定是无条件均值方差有效策略，不过我们利用条件均值方差有效策略给出了一个特殊情况下的无条件均值方差有效策略。
[Abstract]:With the help of stochastic analysis theory developed by Ito, mathematical finance has entered a new era, a large number of stochastic models describing financial markets have been developed, and derivatives pricing problems based on the corresponding financial market models have been developed. The problem of portfolio optimization is solved one by one. Different from focusing on the study of market structure, behavioral finance theory focuses on the differences of market participants themselves. It also notes the influence of asymmetric information on investors' decision-making, but the difference in information is difficult to describe by mathematical models, so that related studies focus on descriptive analysis. Different descriptive analysis, In this paper, we try to depict the difference of some kind of information in mathematics. The problem of portfolio optimization for investors with different information when given information is solved in a market model with state transition. This paper first explains how information affects people's decision-making behavior by means of a game. In this game, different players know different information, which directly results in them being under the same game goal. The strategy used was completely different. And then we turned our attention to our real research object, the capital market, and we first built a market model based on the real market, in which there were risky bonds. Cyclical industry stocks, and aperiodic industry stocks, and then we mathematically describe several different types of typical investors that correspond to real market investors. The difference between different investors is their ability to access and process information that can have a significant impact on the market. So the information they have when they make investment decisions is different. We use the HJB equation method to give the mean mean variance and mean variance of different investors under the condition of their respective information, and the corresponding efficient boundary. We also reveal the important relationship between conditional mean variance efficient strategy and unconditional mean variance efficient strategy. We find that an investor's unconditional mean and variance efficient strategy must be given the investment. The effective strategy of mean variance under the condition that the person has the information, But not every conditional mean and variance efficient strategy must be unconditional mean and variance efficient. However, we give an unconditional mean variance efficient strategy in a special case by using conditional mean mean variance efficient strategy.
【学位授予单位】：清华大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F830.59

【共引文献】