在部分信息下的投资组合选择问题的研究

发布时间：2018-02-07 13:05

本文关键词： 投资组合部分信息随机LQ控制泊松过程 Markov体制转换非线性滤波 HJB方程　出处：《西安工程大学》2013年硕士论文　论文类型：学位论文

【摘要】：在现代金融市场中考虑信息对投资组合的影响是至关重要的，论文主要内容是对部分信息下的证券投资组合选择模型的研究。证券的投资本质上可以分为风险投资(例如:股票)和无风险投资(例如:债券)，能够合理分配风险资产和无风险资产投资的比例，使投资者获得最大的收益，这就是所谓投资者寻找的最优投资策略。实际的投资组合问题中股票价格所满足的随机微分方程中的漂移系数往往是不能被直接观测到的，投资者观测到的仅仅是股票价格。这就是本文中所说的部分信息。论文主要研究对象是针对这种部分信息情况下的投资组合问题进行研究。全文内容共分为六章： (1)第一章介绍了部分信息下的投资组合选择问题的研究现状及研究意义，并简单介绍了本论文所要解决的问题和主要研究内容。 (2)第二章主要介绍了在论文研究过程当中应用到的主要工具，涉及的重要定理、引理和定义。 (3)第三章主要研究了在部分信息下的投资组合问题，其中模型中的股票价格不仅由布朗运动驱动，而且受到马尔科夫调制参数的影响，运用非线性滤波估计技术对平均收益率进行估计，使其模型转化为完全信息下的模型，考虑指数和对数两种效用函数下，运用随机控制的方法，分别对其最优策略进行求解。 (4)第四章主要研究了部分信息下，投资组合效用最大化的问题。其中，风险资产（股票）价格满足跳扩散过程，此过程中的系数受马尔科夫调制参数的影响。通过运用非线性滤波技术，将部分信息的问题转化为完全信息的问题。最终在均值-方差准则下计算出最优投资策略。 (5)第五章主要研究的是在部分信息的情况下，股票价格不仅由布朗运动驱动，而且受到泊松过程的驱动。对于不可观测的信息，运用非线性滤波估计技术对平均收益率进行估计，，并且给出了具体表达形式。最后，运用随机LQ控制的方法，对投资组合问题的最优策略进行求解。 (6)第六章主要是对全文进行总结，以及给出今后研究工作的方向。
[Abstract]:It is essential to consider the impact of information on the portfolio in modern financial markets, The main content of this paper is to study the portfolio selection model under partial information. The investment of securities can be divided into venture capital (for example, stock) and risk-free investment (E. G. bond), which can be allocated reasonably. The ratio of risky assets to risk-free investments, This is called the optimal investment strategy that investors seek. The drift coefficients in stochastic differential equations of stock prices in real portfolio problems are often not directly observed. The investors only observe the stock price. This is part of the information in this paper. The main research object of this paper is to study the portfolio problem under the condition of this kind of partial information. The full text is divided into six chapters:. The first chapter introduces the research status and significance of portfolio selection under partial information, and briefly introduces the problems to be solved and the main research contents in this paper. Chapter 2 mainly introduces the main tools, important theorems, Lemma and definitions applied in the research process. In Chapter 3, we mainly study the portfolio problem under partial information, in which the stock price in the model is not only driven by Brownian motion, but also influenced by Markov modulation parameters. The nonlinear filter estimation technique is used to estimate the average rate of return, and the model is transformed into a model with complete information. Considering the exponential and logarithmic utility functions, the optimal strategy is solved by using the stochastic control method. Chapter 4th mainly studies the problem of portfolio utility maximization under partial information. The coefficients in this process are influenced by Markov modulation parameters. By using nonlinear filtering technique, the problem of partial information is transformed into a problem of complete information. Finally, the optimal investment strategy is calculated under the mean-variance criterion. Chapter 5th focuses on the case of partial information, where stock prices are driven not only by Brownian motion, but also by Poisson processes. The nonlinear filter estimation technique is used to estimate the average return rate, and the concrete expression is given. Finally, the optimal strategy of the portfolio problem is solved by using the stochastic LQ control method. Chapter 6th summarizes the full text and gives the direction of future research.
【学位授予单位】：西安工程大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.91;O211.6

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