通货膨胀影响下的最优消费投资策略研究

发布时间：2019-02-14 10:53

【摘要】：摘要：利用随机数学研究未定环境下的最优消费投资问题已成为金融数学中一个重要的领域。首先由Merton建立的连续时间下的投资组合模型为以后的研究提供了十分重要的理论基础。基于现实的金融市场往往是一个不完备的市场,因此引入有实际意义的约束条件来研究最优投资组合问题,具有重要的理论和现实意义。为了建立更加符合实际的资产价格模型,本文主要考虑了通货膨胀这一重要因素,并在存在通货膨胀这一假设的情形下,来研究最优消费和投资组合问题的最优策略选择问题。首先,本论文简要地综述了现代投资组合理论的背景、研究意义以及一些国内外的相关研究现状；其次,介绍了与本论文相关的一些基本理论知识,主要包括效用函数,布朗运动,伊藤公式,随机控制理论；然后,我们给出了在通货膨胀影响下的资产价格模型,利用随机控制原理得到了在通货膨胀影响下的最优消费和投资组合模型的解；最后,本文讨论了在效用函数分别为常数相对风险厌恶和绝对风险厌恶的情形下的资产价格模型,利用随机动态规划原理得到了最优策略的显式解。结果表明：投资者的终端财富期望与通货膨胀密切相关,即当风险证券波动率与通货膨胀波动率是负相关关系时,投资者为了应对通货膨胀带来的不利影响,应该相应地增加其在风险证券上的投资比例。
[Abstract]:Absrtact: it has become an important field in financial mathematics to study the optimal consumption and investment problem in uncertain environment by using stochastic mathematics. Firstly, the continuous time portfolio model established by Merton provides a very important theoretical basis for future research. The financial market based on reality is often an incomplete market, so it is of great theoretical and practical significance to introduce practical constraints to study the optimal portfolio problem. In order to establish a more realistic asset price model, this paper mainly considers inflation as an important factor, and studies the optimal strategy selection problem for optimal consumption and portfolio problems under the assumption of inflation. First of all, this paper briefly summarizes the background of the modern portfolio theory, the significance of the research and some domestic and foreign related research status; Secondly, some basic theories related to this paper are introduced, including utility function, Brownian motion, Ito formula and stochastic control theory. Then, we give the asset price model under the influence of inflation, and obtain the solution of the optimal consumption and investment portfolio model under the influence of inflation by using the stochastic control principle. Finally, this paper discusses the asset price model under the condition that the utility function is constant relative risk aversion and absolute risk aversion, and obtains the explicit solution of the optimal strategy by using the stochastic dynamic programming principle. The results show that the end-wealth expectation of investors is closely related to inflation, that is, when the volatility of risky securities is negatively related to inflation volatility, investors will deal with the adverse effects of inflation. The proportion of investments in risky securities should be increased accordingly.
【学位授予单位】：中南大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F822.5;F832.48

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