基于g-期望的组合选择问题研究
关键词 g-期望 组合选择 均值-方差模型 效用函数
毕业设计说明书（论文）外文摘要
Title Portfolio selection problem based on g-expectation
Abstract
Markowitz published “Portfolio Selection” in 1952, then the Portfolio problem has always been an issue of concern to many academics and investors. Also based on the mean-variance model, many academics make many different assumptions about the distribution of the capital market yields and establish the corresponding models which are in line with the current situation and more acceptable to investor. With the development of econometrics, the academics are no longer limited to the simple linear regression models, but gradually turned to a variety of nonlinear models. In 1997, through the research of the theory of expectation effect, Peng introduces a kind of nonlinear expectation, g-expectation and conditional g-expectation by nonlinear backward differential equation. From then on, people have realized the strong application significance of g-expectation. In the paper, I mainly establish the portfolio selection model which based on the g-expectation under the existing work and take the special functions to simplify solving and analysis.
Keywords g-expectation, portfolio selection, mean-variance model, utility function
目 次
1. 绪论 1
1.1 选题背景和研究意义 1
1.2 研究现状 2
1.3 本文内容 5
1.4 创新点 5
2. 模型的建立 6
2.1 模型建立的前期准备 6
2.1.1 组合选择问题的数学描述 6
2.1.2 效用函数 7
2.1.3 g-期望的发展 8
2.2 模型的建立 8
3. 模型的求解与分析 13
3.1 模型的求解 13
3.2 模型的分析 18
3.2.1 模型的扩展1 18
3.2.2 模型的扩展2 19
3.3 模型的经济涵义 21
结 论 24
致 谢 26
参考文献 27
1. 绪论
1.1 选题背景和研究意义
1952年，Markowitz 在《Journal of Finance》中发表了《Portfolio Selection》，在这篇著作中Markowitz最早采用了均值-方差模型来研究资产的投资组合选择问题，他首次采用收益率的均值、方差来量化资产的收益和风险。该著作奠定了投资组合理论的基础，标志着现代组合投资理论的开端。从此，投资组合理论成为金融问题研究的主要领域之一，并且在众多学者的研究下快速发展。