期望效用最大化下的投资组合模型研究

发布时间：2018-01-01 16:19

本文关键词：期望效用最大化下的投资组合模型研究　出处：《广西大学》2014年硕士论文　论文类型：学位论文

【摘要】：投资组合模型的构建不仅对投资者的最优投资决策起到至关重要的指导作用,也是金融经济学,特别是资产定价研究领域的重要问题之一.现实资本市场中存在着许多随机不确定因素,面对这些不确定问题最有效的研究方法就是期望效用理论.期望效用理论认为投资者在投资过程中所追求的并不是最终能够获得的财富水平,而是最终能够获得的期望效用.本文主要基于期望效用最大化的目标来建立投资组合模型,主要研究内容和成果如下： (1)当效用函数是CARA型效用函数时,通过对期望财富效用函数的泰勒展开,得到了高阶矩风险与期望财富效用的关系：偏度与期望财富效用是正相关的；峰度与期望财富效用是负相关的,以及当效用函数是二次函数且收益服从正态分布时均值-方差模型与期望效用模型等价.随后,文中建立了CARA型效用函数静态模型并给出简化的隐式解. (2)面对非随机的不确定因素时,模糊理论比期望效用理论更加合理.文中用可能性均值和可能性方差度量投资组合的收益和风险,构建了带有流动性的模糊投资组合模型,用Lagrange乘子法求出其最优解,并给出数值结果. (3)基于投资者投资周期内累积的期望效用最大化的目标,文中在三种不同的假设环境中分别建立了对应的动态投资组合模型.从三个模型的最优决策中可以得到以下规律：最优投资比例不受投资者财富水平、消费水平和非资本收入水平的影响；最优消费水平取决于投资者的财富水平.
[Abstract]:The construction of portfolio model not only plays an important role in guiding investors' optimal investment decision, but also plays an important role in financial economics. In particular, one of the most important problems in the field of asset pricing is the existence of many random uncertainties in the real capital market. In the face of these uncertainties, the most effective research method is expected utility theory, which holds that what investors are pursuing in the process of investment is not the level of wealth that can be obtained in the end. This paper is based on the goal of maximizing expected utility to establish a portfolio model, the main research content and results are as follows: 1) when utility function is CARA type utility function, Taylor expansion of expected wealth utility function is adopted. The relationship between higher moment risk and expected wealth utility is obtained: bias is positively related to expected wealth utility; The kurtosis is negatively correlated with the expected wealth utility, and the mean-variance model is equivalent to the expected utility model when the utility function is a quadratic function and the income is from the normal distribution. In this paper, the static model of utility function of CARA type is established and the simplified implicit solution is given. In the face of non-random uncertainty, fuzzy theory is more reasonable than expected utility theory. In this paper, the probability mean and possibility variance are used to measure the return and risk of the investment portfolio. A fuzzy portfolio model with liquidity is constructed. The optimal solution is obtained by Lagrange multiplier method and the numerical results are given. Based on the objective of maximizing the expected utility accumulated in the investor's investment cycle. In this paper, the corresponding dynamic portfolio models are established in three different hypothetical environments. From the optimal decision of the three models, the following laws can be obtained: the optimal investment ratio is not subject to the wealth level of the investors. The influence of consumption level and non-capital income level; The optimal level of consumption depends on the level of wealth of investors.
【学位授予单位】：广西大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F830.59;O225

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