在Knight不确定和部分信息下最优消费投资问题研究

发布时间：2018-01-07 06:36

本文关键词：在Knight不确定和部分信息下最优消费投资问题研究　出处：《安徽工程大学》2013年硕士论文　论文类型：学位论文

【摘要】：在金融数学领域中,最优消费投资问题研究是最基本的内容之一,已被国内外众多学者所研究.在现实的经济环境下,不仅要考虑部分信息对最优消费投资决策的影响,还要考虑投资者对未来投资前景所持态度的不同而造成的最优消费投资决策的差异.本文在奈特不确定和部分信息下,运用随机最优控制的方法,建立最优消费投资模型.从而我们可以导出使得投资者消费和终端财富期望效用最大化的最优交易策略.这些理论的建立可以很好地指导实际. 本文首先讨论了在部分信息下股票支付红利的最优交易策略.考虑一个多种股票模型,股票价格过程满足随机微分方程,股票价格的瞬时收益率由有限状态连续时间的马尔科夫链刻画.在投资者终端财富预期效用最大化目标下,利用隐马尔科夫模型(HMM)滤波理论和Malliavin分析,导出最优交易策略的显式表达式.其次在上述内容的基础上研究了在奈特不确定框架下的最优交易策略.文中刻画了α-最大最小期望效用(α-MEU).该模型的主要特征是分离了含糊和含糊态度,其中含糊被刻画为决策者的主观信仰,而含糊态度被刻画为决策者的含糊品味.在奈特不确定投资者a-最大最小期望效用最大化目标下,求解出最优交易策略.最后研究了在均值回复利率下奈特不确定投资者的最优消费投资策略.文中采用递推多先验效用,给出了α-MEU的表达式,导出了在幂效用下利率为均值回复过程的最优投资组合. 通过上述问题的研究,使得我们的模型较传统的Merton模型更加完善,更加符合实际,这对投资者在市场中选择最优消费投资策略具有一定的现实指导作用.
[Abstract]:In the field of financial mathematics, the study of optimal consumption and investment is one of the most basic contents, which has been studied by many scholars at home and abroad. We should not only consider the influence of some information on the optimal consumption and investment decision. Considering the difference of the optimal consumer investment decision caused by the different attitude of the investors to the future investment prospects, this paper uses the stochastic optimal control method under the Knight uncertainty and partial information. By establishing the optimal consumption and investment model, we can derive the optimal trading strategy that maximizes the expected utility of investors' consumption and terminal wealth. The establishment of these theories can well guide the practice. In this paper, we first discuss the optimal trading strategy of dividend payment under partial information. Considering a variety of stock models, the stock price process satisfies the stochastic differential equation. The instantaneous return rate of stock price is characterized by Markov chain of finite state continuous time, under the goal of maximizing expected utility of investor terminal wealth. The hidden Markov model (hmm) filtering theory and Malliavin analysis are used. The explicit expression of the optimal trading strategy is derived. Secondly, the optimal trading strategy under the framework of Knight uncertainty is studied on the basis of the above contents. The 伪 -maximum and minimum expected utility (伪 -MEUU) is characterized in this paper. The main feature of the model is the separation of ambiguity and ambiguity. Ambiguity is described as the subjective belief of the decision-maker, and the vague attitude is characterized as the vague taste of the decision-maker. In the case of Knight's uncertain investor a-maximum expected utility maximization goal. Finally, the optimal consumer investment strategy of Knight uncertain investors under the mean return interest rate is studied. In this paper, the expression of 伪 -MEU is given by using recursive multi-priori utility. The optimal portfolio with the interest rate as the mean return process is derived under the power utility. Through the study of the above problems, our model is more perfect than the traditional Merton model, more in line with the reality. This has a certain practical guiding role for investors to choose the optimal consumption and investment strategy in the market.
【学位授予单位】：安徽工程大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.59;F224

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