摩擦市场下的M-CVaR投资组合优化研究

发布时间：2018-06-19 22:50

本文选题：均值-CVaR + 均值-下半方差　；参考：《武汉科技大学》2014年硕士论文

【摘要】：马科维兹提出的均值-方差模型是投资组合理论发展的开端，随后越来越多的学者在此基础上提出了新的想法和模型，不断完善形成现代投资理论。在投资组合的理论中，选择风险的量化方法一直是要解决的问题之一，国内外学者针对此问题提出了许多风险度量的方法，其中VaR近年来得到了广泛的关注，然而VaR不满足次可加性，不一定满足凸性且VaR的前提条件是假设市场是正常的，因此对于某些极端情况，VaR显得束手无策。因此CVaR风险度量方法的产生弥补了VaR的不足。本文从影响金融市场的三个摩擦因子研究了M-CVaR的投资组合模型，一是考虑了借贷利率不同时M-CVaR的投资组合模型，分析了当借贷利率相同以及不同时的情况，最后利用二次序列规划的方法以及旋转算法对模型进行分析和求解并获得了最优的投资策略。二是考虑了非光滑凹交易费用的M-CVaR投资组合模型，研究了实际中根据投资比例的不同划分的分段交易成本对投资决策的影响，并利用线性拟合求解模型。三是考虑了基数约束的M-CVaR投资组合模型，加入了非线性隶属度函数，研究了投资者的满意度，利用CPLEX软件求解0-1混合整数规划问题，求出最优投资策略，，具有一定的有效性和实用性。三个不同的角度解释了不同的摩擦因子对市场的影响不同，有利于投资者在投资过程时考虑不同的摩擦因素时给予有效的建议。
[Abstract]:The mean-variance model put forward by Markowitz is the beginning of the development of portfolio theory, and then more and more scholars put forward new ideas and models on this basis, and form modern investment theory. In the theory of portfolio, choosing the quantitative method of risk is always one of the problems to be solved. Scholars at home and abroad have put forward a lot of risk measurement methods, among which VaR has been paid more and more attention in recent years. However, VaR does not satisfy subadditivity and convexity, and the premise of VaR is to assume that the market is normal, so VaR is helpless for some extreme cases. Therefore, the generation of CVaR risk measurement method makes up for the shortage of VaR. In this paper, the portfolio model of M-CVaR is studied from three frictional factors which affect the financial market. Firstly, the portfolio model of M-CVaR with different lending rate is considered, and the situation of the same and different borrowing rates is analyzed. Finally, the quadratic sequential programming method and rotation algorithm are used to analyze and solve the model, and the optimal investment strategy is obtained. Secondly, the M-CVaR portfolio model with non-smooth concave transaction cost is considered, and the influence of segmented transaction cost on investment decision is studied according to the different proportion of investment in practice, and the linear fitting is used to solve the model. Thirdly, the M-CVaR portfolio model with cardinality constraints is considered, the nonlinear membership function is added, the satisfaction of investors is studied, the 0-1 mixed integer programming problem is solved by CPLEX software, and the optimal investment strategy is obtained. It has certain validity and practicability. Three different angles explain the influence of different friction factors on the market, which is helpful for investors to give effective advice when considering different friction factors in the process of investment.
【学位授予单位】：武汉科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224

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