股价波动率不确定下的最优消费与投资问题研究

发布时间：2018-01-14 04:04

本文关键词：股价波动率不确定下的最优消费与投资问题研究　出处：《安徽工程大学》2014年硕士论文　论文类型：学位论文

【摘要】：关于最优消费和投资问题的研究,诸多学者更是在许多方面进行了孜孜不倦地探索,但大多数模型都是基于风险资产(股票)价格波动率为常数的假设。随着金融市场的不断创新和改善,对更加符合实际的模型进行研究已不容忽视。本文基于现有的理论成果,首先,在连续时间模型假设下,研究股票价格波动率具有模型不确定对投资者的最优消费和投资策略的影响,通过求解HJB方程得到最优策略,并在常相对风险厌恶效用的情形下,获得最优消费和投资的显式解,进而得到含糊厌恶的投资者是基于股价波动率的上界作出决策,并对所得结果进行数值模拟和经济分析。其次,在通胀环境下,研究股票价格波动率具有奈特不确定时对投资者的最优消费和投资策略的影响,获得通胀环境下投资者的最优投资和消费策略的显式解,并对所得结果进行数值模拟和经济分析。最后,研究通胀服从均值回复过程时投资者的最优消费和投资问题,在给定通胀服从的均值回复过程的微分方程与常相对风险厌恶效用的情形下,得到投资者的最优投资和消费策略。本文表明了奈特不确定、通胀和均值回复均会对投资者的最优消费和投资产生影响。因此,本文的理论价值在于股价波动率不确定时获得了投资者的最优消费和投资策略的显式解,并给出了含糊厌恶的投资者都是基于股价波动率的上界作出决策的。由于本文模型较传统模型更加完善,更加符合实际,对投资者在市场中选择最优消费和投资策略具有一定的现实指导作用,所以本模型较传统模型具有一定的实际应用价值。
[Abstract]:Study on optimal consumption and investment problem, many scholars are in many aspects of the exploration diligently, but most of the models are based on risk assets (stock) price volatility is the assumption of a constant. With the continuous innovation and improvement of the financial market, to study more realistic models can not be ignored.
This paper is based on the existing theoretical results, first of all, in a continuous time model, stock price volatility has uncertain effect on the model of optimal consumption and investment strategy of investors, the optimal strategy by solving the HJB equation and the constant relative risk aversion utility case, explicit optimal consumption and investment solutions and then get the ambiguity averse investor is making decisions based on the upper bound of stock price volatility, and analyzing the results of numerical simulation and economy. Secondly, in an inflationary environment, influence of the stock of the optimal consumption and investment strategy of investors price volatility with Knightian uncertainty, investors have explicit inflation environment the optimal investment and consumption strategies, and analyzing the results of numerical simulation and economic research. Finally, inflation follows the mean reversion process investors most Optimal consumption and investment problem, return differential equation process and constant relative risk aversion utility in the case of a given subject under the mean inflation, investors get the optimal investment and consumption strategies. This paper shows that the Knightian uncertainty, inflation and mean reversion will impact on the optimal consumption and investment of investors.
Therefore, the value of this paper lies in the volatility of stock market uncertainty to obtain explicit optimal consumption and investment strategy for investors of the solution, and gives the ambiguity averse investors are making decisions based on the upper bound of stock price volatility. Because this model is more perfect than the traditional model, more practical and has some practical guiding significance for investors to choose the optimal consumption and investment strategy in the market, so this model is better than the traditional model has a certain practical value.

【学位授予单位】：安徽工程大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F830.91;F224

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