最优投资组合问题的模糊决策方法

发布时间：2018-05-05 18:11

本文选题：投资组合问题 + 模糊决策　；参考：《西安电子科技大学》2014年硕士论文

【摘要】：近年来，一方面投资组合问题中的实际因素往往具有一定的模糊性，另一方面带交易费用、限制买空、卖空等条件的投资组合优化问题是一个NP-完全问题，因此，对投资组合问题采用模糊理论与决策方法、智能优化算法来求解成为研究重点与热点。本文采用模糊决策方法及混合智能算法解决带约束的股票-债券投资组合问题。主要工作如下： 1.针对带有V-型交易费用的半绝对偏差风险函数投资组合问题，利用模糊决策理论，提出了一种新的投资收益目标水平和投资风险目标水平心理满意度的非线性隶属函数，并将满足非线性满意程度的投资组合选择模型转化为线性规划模型，，证明了两者的等价性，最后通过实例说明了所建模型的可行性与有效性。 2.针对证券交易市场中交易单位、交易费用等约束，给出了股票-债券的半绝对偏差风险函数，建立了在不允许买空、卖空、缴纳交易费用及交易单位约束的条件下的股票-债券投资组合选择的数学模型，提出了布谷鸟算法与萤火虫算法相结合的混合智能算法，优势互补，增强了全局寻优能力。最后通过实例验证了模型及算法的有效性。
[Abstract]:In recent years, on the one hand, the actual factors in portfolio problems are often fuzzy, on the other hand, the portfolio optimization problem with transaction cost, short buying, short selling and other conditions is a NP-complete problem. Fuzzy theory and decision method are used to solve portfolio problem. In this paper, a fuzzy decision method and a hybrid intelligent algorithm are used to solve the stock-bond portfolio problem with constraints. The main tasks are as follows: 1. Aiming at the portfolio problem of semi-absolute deviation risk function with V-type transaction cost, a new nonlinear membership function of psychological satisfaction of investment return target level and investment risk target level is proposed by using fuzzy decision theory. The portfolio selection model satisfying the nonlinear satisfaction degree is transformed into a linear programming model, and the equivalence between the two models is proved. Finally, the feasibility and validity of the model are illustrated by an example. 2. Aiming at the constraints of trading unit and transaction cost in the stock exchange market, the semi-absolute deviation risk function of stock bond is given, and the risk function of short selling and short selling is established. Based on the mathematical model of stock bond portfolio selection under the condition of payment of transaction cost and trading unit constraint, a hybrid intelligent algorithm combining Cuckoo algorithm and firefly algorithm is proposed, which can complement each other and enhance the ability of global optimization. Finally, an example is given to verify the validity of the model and algorithm.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F830.91;O225

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