数学规划在非系统风险组合投资中的应用

发布时间：2018-03-22 01:32

本文选题：数学规划　切入点：罚函数　出处：《中北大学》2017年硕士论文　论文类型：学位论文

【摘要】：数学规划包括线性规划,二次规划,整数规划,混合整数规划,0-1规划,随机规划,模糊规划及多目标规划等。数学规划中的各种模型在求解实际问题中具有十分重要的作用,数学规划模型应用于油井选址,数学建模,交通设计,矿产运输等各个领域,在节约资源,提高效率方面起到了关键性的作用。随着全球经济及金融的快速发展,数学规划模型已广泛应用于资产配置及金融投资领域。本文通过研究数学规划模型在投资组合中的应用,旨在通过最优的组合投资获得最大的经济收益,由于系统风险在金融投资中是不可控制的,由此本文基于非系统风险中的信息风险构建了基于信息风险控制函数的投资组合优化模型。首先考虑了带红利的基于信息风险控制函数的投资组合优化模型,其次考虑了带交易费用的信息控制投资组合模型,然后通过最优化理论中的罚函数算法对模型进行求解。实证研究表明,基于信息控制的投资组合模型比一般的投资组合模型具有较低的收益率,基于信息控制的投资组合模型更倾向于配置信息较透明的资产,通过比较不带交易费用的模型和带交易费用的模型,发现带交易费用的模型得到的收益率较低,带交易费用的投资组合模型倾向于配置较少的资产,以提高整体的收益,随着交易费用比例的增大,目标函数值在逐渐变小,资产配置的分散程度在逐渐变小,由于交易费用的增大,资产收益降低,从而导致投资组合的风险值降低,更加符合实际,希望本文的研究能为研究人员及投资者提供一定的参考。
[Abstract]:Mathematical programming includes linear programming, quadratic programming, integer programming, mixed integer programming 0-1 programming, stochastic programming, fuzzy programming and multi-objective programming. The application of mathematical planning model in oil well location, mathematical modeling, traffic design, mineral transportation and other fields plays a key role in saving resources and improving efficiency. With the rapid development of global economy and finance, The mathematical programming model has been widely used in the field of asset allocation and financial investment. Because systemic risk is beyond control in financial investment, In this paper, a portfolio optimization model based on information risk control function is constructed based on information risk in non-system risk. Firstly, a portfolio optimization model based on information risk control function with dividend is considered. Secondly, the portfolio control model with transaction cost is considered, and then the penalty function algorithm in optimization theory is used to solve the model. The portfolio model based on information control has lower yield than the general portfolio model, and the portfolio model based on information control is more inclined to allocate the assets with more transparent information. By comparing the model without transaction cost and the model with transaction cost, it is found that the model with transaction cost has a lower yield, and the portfolio model with transaction cost tends to allocate less assets to improve the overall income. With the increase of the proportion of transaction cost, the value of objective function becomes smaller, and the degree of dispersion of asset allocation becomes smaller. Because of the increase of transaction cost, the return of assets decreases, which leads to the decrease of risk value of portfolio, which is more in line with the reality. I hope this study can provide some reference for researchers and investors.
【学位授予单位】：中北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O221

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