加权极大—极小随机模糊投资组合及实证研究
发布时间：2019-03-02 09:04
【摘要】：证券市场是一个复杂的动态系统,经济全球化、经济一体化加剧了证券市场的复杂性和波动性。本文把证券收益视为随机模糊变量能够同时反映证券市场随机和模糊的双重不确定性,另外利用现代行为金融理论的研究成果,考虑投资者真实的心理偏好,构建加权极大-极小随机模糊投资组合模型。为了求解模型在市场存在交易费用和最小交易单位情况下投资组合权重,对动态邻居粒子群算法进行改进,提出改进的动态邻居粒子群算法。在我国的经济环境下,利用改进动态邻居粒子群算法对模型求解并检验模型的有效性。论文的研究主要包括 (1)针对证券市场同时存在随机和模糊双重不确定性因素,把证券收益视为随机模糊变量,构建以财富变化量为基础的期望收益隶属度函数。利用加权极大-极小算子,同时考虑投资组合期望收益和目标概率满足投资者期望值的隶属度,构建加权极大-极小随机模糊投资组合模型。利用Markowitz的历史数据研究模型的有效边界,结果表明把证券收益视为随机模糊变量的投资组合与Markowitz均值-方差投资组合有效边界不一致。 (2)针对动态邻居粒子群算法所存在的不足,对算法的粒子群初始化方法和动态邻居的拓扑结构进行改进,提出改进的动态邻居粒子群算法。分别针对无权重约束和有权重约束投资组合对算法迭代寻优能力进行检验,结果表明改进动态邻居粒子群算法能够有效求解投资组合有效边界问题。 (3)随机选取沪深300指数的50支股票作为研究样本,对加权极大-极小随机模糊投资组合模型进行实证检验。实证检验包括两个部分。①在市场无摩擦的环境下,分别比较加权极大-极小随机模糊投资组合、Markowitz均值-方差投资组合和Vercher模糊投资组合的投资绩效,实证结果表明加权极大-极小随机模糊投资组合的投资绩效更优。②在市场存在摩擦的环境下,对不同风险态度的投资者设置不同的投资组合参数,并利用改进动态邻居粒子群算法对模型求解,结果表明加权极大-极小随机模糊投资组合模型能够有效反映不同风险态度投资者的心理偏好。
[Abstract]:The securities market is a complex dynamic system. Economic globalization and economic integration aggravate the complexity and volatility of the securities market. In this paper, the return of securities can be regarded as a random fuzzy variable which can reflect the double uncertainty of random and fuzzy in the stock market at the same time. In addition, by using the research results of modern behavioral finance theory, the real psychological preference of investors is considered. A weighted maximum-minimum stochastic fuzzy portfolio model is constructed. In order to solve the model with transaction cost and minimum trading unit in the market the dynamic neighbor particle swarm optimization algorithm is improved and an improved dynamic neighbor particle swarm algorithm is proposed. In the economic environment of our country, the improved dynamic neighbor particle swarm optimization algorithm is used to solve the model and verify the validity of the model. The main contents of this paper are as follows: (1) in view of the existence of both random and fuzzy uncertainties in the stock market, the securities return is regarded as a random fuzzy variable, and the expected return membership function based on the amount of wealth change is constructed. A weighted maximum-minimum random fuzzy portfolio model is constructed by using the weighted maximum-minimum operator and considering the membership degree of the expected return and target probability of the portfolio to satisfy the expected value of the investor. Using the historical data of Markowitz to study the effective boundary of the model, the results show that the portfolio which regards the return of securities as a random fuzzy variable is not consistent with the effective boundary of the Markowitz mean-variance portfolio. (2) aiming at the deficiency of the dynamic neighbor particle swarm optimization algorithm, the particle swarm initialization method and the topological structure of the dynamic neighbor particle swarm optimization algorithm are improved, and an improved dynamic neighbor particle swarm optimization algorithm is proposed. The iterative optimization ability of the algorithm is tested for unauthorized and weighted constrained portfolio respectively. The results show that the improved dynamic neighbor particle swarm optimization algorithm can effectively solve the portfolio efficient boundary problem. (3) 50 stocks of Shanghai-Shenzhen 300 index are randomly selected as research samples, and the weighted maximum-minimum stochastic fuzzy portfolio model is empirically tested. The empirical test consists of two parts. 1 under the condition of no friction in the market, we compare the investment performance of weighted maximum-minimum random fuzzy portfolio, Markowitz mean-variance portfolio and Vercher fuzzy portfolio, respectively, and compare the investment performance of weighted maximum-minimum random fuzzy portfolio, Markowitz mean-variance portfolio and Vercher fuzzy portfolio, respectively. The empirical results show that the investment performance of weighted maximum-minimum random fuzzy portfolio is better. 2 under the environment of market friction, different portfolio parameters are set for investors with different risk attitudes. The improved dynamic neighbor particle swarm optimization algorithm is used to solve the model. The results show that the weighted maximum-minimum stochastic fuzzy portfolio model can effectively reflect the psychological preferences of investors with different risk attitudes.
【学位授予单位】：东北大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F830.59;F224
本文编号：2432904
[Abstract]:The securities market is a complex dynamic system. Economic globalization and economic integration aggravate the complexity and volatility of the securities market. In this paper, the return of securities can be regarded as a random fuzzy variable which can reflect the double uncertainty of random and fuzzy in the stock market at the same time. In addition, by using the research results of modern behavioral finance theory, the real psychological preference of investors is considered. A weighted maximum-minimum stochastic fuzzy portfolio model is constructed. In order to solve the model with transaction cost and minimum trading unit in the market the dynamic neighbor particle swarm optimization algorithm is improved and an improved dynamic neighbor particle swarm algorithm is proposed. In the economic environment of our country, the improved dynamic neighbor particle swarm optimization algorithm is used to solve the model and verify the validity of the model. The main contents of this paper are as follows: (1) in view of the existence of both random and fuzzy uncertainties in the stock market, the securities return is regarded as a random fuzzy variable, and the expected return membership function based on the amount of wealth change is constructed. A weighted maximum-minimum random fuzzy portfolio model is constructed by using the weighted maximum-minimum operator and considering the membership degree of the expected return and target probability of the portfolio to satisfy the expected value of the investor. Using the historical data of Markowitz to study the effective boundary of the model, the results show that the portfolio which regards the return of securities as a random fuzzy variable is not consistent with the effective boundary of the Markowitz mean-variance portfolio. (2) aiming at the deficiency of the dynamic neighbor particle swarm optimization algorithm, the particle swarm initialization method and the topological structure of the dynamic neighbor particle swarm optimization algorithm are improved, and an improved dynamic neighbor particle swarm optimization algorithm is proposed. The iterative optimization ability of the algorithm is tested for unauthorized and weighted constrained portfolio respectively. The results show that the improved dynamic neighbor particle swarm optimization algorithm can effectively solve the portfolio efficient boundary problem. (3) 50 stocks of Shanghai-Shenzhen 300 index are randomly selected as research samples, and the weighted maximum-minimum stochastic fuzzy portfolio model is empirically tested. The empirical test consists of two parts. 1 under the condition of no friction in the market, we compare the investment performance of weighted maximum-minimum random fuzzy portfolio, Markowitz mean-variance portfolio and Vercher fuzzy portfolio, respectively, and compare the investment performance of weighted maximum-minimum random fuzzy portfolio, Markowitz mean-variance portfolio and Vercher fuzzy portfolio, respectively. The empirical results show that the investment performance of weighted maximum-minimum random fuzzy portfolio is better. 2 under the environment of market friction, different portfolio parameters are set for investors with different risk attitudes. The improved dynamic neighbor particle swarm optimization algorithm is used to solve the model. The results show that the weighted maximum-minimum stochastic fuzzy portfolio model can effectively reflect the psychological preferences of investors with different risk attitudes.
【学位授予单位】：东北大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F830.59;F224
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