带交易费用的模糊投资组合理论

发布时间：2018-01-13 20:40

本文关键词：带交易费用的模糊投资组合理论　出处：《湘潭大学》2014年硕士论文　论文类型：学位论文

【摘要】：自从Markowitz把数学的思想引入到投资组合中，投资组合就成为了一个热门的研究方向，由于投资环境的复杂性和不稳定性，，使得研究者很难完整的去建立一个投资组合模型。于是，不同的研究从不同的角度去建立一个时候的模型，用不同的数学的思想来解决投资组合问题。本文基于区间规划的基础上，研究了在不同的交易费用情况下的模糊投资组合。在对区间数进行估值时，引进了正态隶属函数，并且在修正未来回报额时，考虑了一个符合实际情况的因素涨跌停板；同时，引进了新的流动性的定义方法，改正了以往用换手率研究带来的缺陷。通过以上的方法，建立新的在不同交易费下可调整策略的模糊投资组合模型。第一章主要介绍了模糊投资组合问题和人工鱼群算法的研究背景和研究现状。第二章陈述一般的投资组合，介绍了一些关于的未来收益，偏好因子，和流动性等下文建立模型和解决模型所要用到的知识点。第三章建立了一个带固定交易费用的投资组合模型，该模型采用了绝对偏差作为风险函数，通过不断的变形，将其转化为一个线性的模型。第四章建立了一个交易费用为凸函数的投资组合模型，该模型中涉及到了区间数，故在模型转化的时候用到了区间数的计算。第五章通过从上海证券交易市场选取5支不同的股票，通过人工鱼群算法进行了数据模拟，得到了在不同的风险偏好下投资者组合。
[Abstract]:Since Markowitz introduced the idea of mathematics into the portfolio, portfolio has become a hot research direction, because of the complexity and instability of the investment environment. It is very difficult for researchers to build a portfolio model completely. Therefore, different studies from different angles to build a time model, using different mathematical ideas to solve the portfolio problem. In this paper, based on interval programming, we study the fuzzy portfolio under different transaction costs. When we estimate the interval number, we introduce the normal membership function and revise the future return amount. A factor in line with the actual situation is considered. At the same time, a new definition method of liquidity is introduced, which corrects the defects brought by the previous research on turnover rate. Through the above methods, a new fuzzy portfolio model with adjustable strategies under different transaction costs is established. The first chapter mainly introduces the research background and present situation of fuzzy portfolio problem and artificial fish swarm algorithm. The second chapter describes the general portfolio, introduces some of the future returns, preference factors, and liquidity, and so on the following models and solutions to the need to use the knowledge. In chapter 3, a portfolio model with fixed transaction costs is established. The model adopts absolute deviation as a risk function and transforms it into a linear model through constant deformation. In Chapter 4th, a portfolio model with convex transaction cost is established. The interval number is involved in the model, so the calculation of the interval number is used in the transformation of the model. Chapter 5th selects five different stocks from Shanghai Stock Exchange and simulates the data by artificial fish swarm algorithm and obtains the investor portfolio under different risk preference.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：O212.1;F830.91

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