菌群优化算法在投资组合中的应用

发布时间：2018-05-14 04:32

本文选题：投资组合 + 风险价值　；参考：《广东商学院》2013年硕士论文

【摘要】：风险价值(Value-at-Risk，VaR)是衡量金融市场风险的主要指标，却不满足次可加性和凸性。条件风险价值(Conditional Value-at-Risk，CVaR)，因具备良好的统计性质弥补了VaR的不足，成为衡量投资组合风险的重要指标。均值 CVaR模型，在给定组合预期收益的前提下，，研究满足CVaR最小的约束条件时组合内各股票的投资权重配置，是一个非线性规划问题。特别是当数据多、维数多时，传统数值优化算法的求解难度增加，求解时间也随之增长，所以遗传算法、粒子群算法等智能算法被引入投资组合优化问题中并取得较好的效果。菌群优化算法作为新兴的群智能算法，因具备良好的性能而被成功用于工程、控制等许多实际优化问题中，但是在投资组合优化领域的运用还很少见。本文重点研究菌群优化算法及其改进对于均值 CVaR模型的求解，取得的主要结论有：（1）改进原始菌群优化算法的趋化操作，使得原来固定不变的趋化步长可以进行自适应修正，同时，细菌个体在寻优过程中不再是随机翻转，而是实现双向游动，进而提高了算法的搜索效率。（2）选取深证A股10只股票进行实际算例分析，将改进前后的菌群优化算法分别用于对均值 CVaR模型的有效求解，并将求解结果加以比较，证明：改进后的菌群优化算法稳定性更强，求解结果更优，可以使得VaR和CVaR两个指标值均变小，从而降低了投资组合的风险。
[Abstract]:Value-at-Risker-VaR is the main index to measure financial market risk, but it is not satisfied with subadditivity and convexity. Conditional Value-at-Riskie Cvar Rao, because of its good statistical properties, makes up for the deficiency of VaR and becomes an important index to measure portfolio risk. The mean value CVaR model is a nonlinear programming problem to study the allocation of the investment weights of each stock in the portfolio when the minimum constraint condition of the portfolio is satisfied under the premise of the expected return of the portfolio. Especially when there are more data and more dimensions, the traditional numerical optimization algorithm is more difficult to solve, and the solving time also increases. Therefore, genetic algorithm, particle swarm optimization and other intelligent algorithms are introduced into the portfolio optimization problem and obtain better results. As a new swarm intelligence algorithm, bacterial colony optimization algorithm has been successfully used in many practical optimization problems, such as engineering, control and so on, because of its good performance. However, its application in portfolio optimization is still rare. In this paper, we focus on the optimization algorithm of microflora and its improvement to solve the mean value CVaR model. The main conclusions are as follows: 1) improving the chemotaxis operation of the original microbial colony optimization algorithm, so that the original fixed chemotaxis step size can be adaptively corrected. At the same time, the bacterial individual is no longer a random flipping in the optimization process, but realizes a two-way walk. Furthermore, the search efficiency of the algorithm is improved. In this paper, 10 stocks of Shenzhen A-share are selected for practical example analysis. The improved microflora optimization algorithm is used to solve the mean value CVaR model effectively, and the results are compared. It is proved that the improved microbial colony optimization algorithm is more stable and the solution result is better, which can reduce the value of VaR and CVaR, thus reducing the risk of portfolio investment.
【学位授予单位】：广东商学院
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：TP301.6;F832.51

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