几类投资组合优化模型及其算法

发布时间：2018-06-19 08:16

本文选题：投资组合优化 + 人工蜂群算法　；参考：《西安电子科技大学》2012年博士论文

【摘要】：投资组合优化问题作为现代金融学的一个核心课题，主要研究如何在不确定情况下对金融资产进行合理配置与选择，从而实现收益率最大化与风险最小化间的均衡．1952年，美国经济学家HarryM.Markowitz在《TheJournalofFinance》杂志上发表了“PortfolioSelection”一文，首次使用证券收益方差度量风险，提出了均值-方差投资组合选择理论，被学术界公认为开创了现代投资组合理论的先河，奠定了定量化研究金融投资问题的基础．随着现代数学方法的发展及应用数学方法研究金融经济问题的金融数学的问世，使得现代金融投资理论开始摆脱纯粹经验化操作和单纯描述性研究的状态，进入了定量分析这一高级阶段，并为投资者进行投资决策提供了指导．当今世界经济飞速发展，金融危机和市场波动频繁出现，我国的资本市场虽然在改革开放之后得到长足发展，但还不太完善和成熟，使得投资者面临越来越多错综复杂的金融投资决策的理论和实践问题，对投资组合优化问题的研究也越来越具有重要的理论和现实意义．本文从以下三个方面开展研究工作，，一是带有基数约束的投资组合优化问题，二是带有交易费用的动态投资组合优化问题，三是投资组合随机优化模型的情景生产方法比较．主要工作如下： 1.人工蜂群算法是近几年提出的一种新的群智能算法，在求解多峰高维函数优化问题时体现出了更为优良的性质．考虑到人工蜂群算法的这一优点，利用人工蜂群算法研究了带有基数约束的投资组合优化模型．通过数值试验可以发现，人工蜂群算法在求解这一问题时，比别的智能优化算法体现出一些更优越的性态． 2.针对带有基数约束的投资组合优化问题，提出一种改进人工蜂群算法．在算法中，利用Deb选择策略使最优解满足约束条件，并引入新的搜索策略以提高算法的收敛速度；同时，使用Bolzmann选择概率来维护种群多样性，防止算法早熟．通过对测试问题的数值实验，表明使用该算法能获得更好的投资策略，有效分散投资组合风险，并说明该算法对于求解投资组合优化问题是快速有效的． 3.研究了存在固定交易费用和比例交易费用情况下的多阶段均值-方差投资组合优化问题．应用离散时间动态规划方法，给出了投资者的间接效用函数、无交易区域边界和有效前沿的解析解，从而确定了投资者的长期最优投资策略．通过数值试验描述了问题的求解过程，并说明了交易费用对有效前沿的影响． 4.研究了连续时间情形下，带有固定交易费用和比例交易费用的均值-方差投资组合优化问题．通过使用动态规划方法，推导出了原问题的Hamilton-Jacobi-Bellman方程，并得到了方程的显式解．从而，推导出原均值-方差问题的最优投资策略和有效前沿的表达式．数值试验给出了交易费用的变化对交易区域和有效前沿的影响，并说明了所给方法的可行性和有效性． 5.比较研究了四种情景生成方法在求解投资组合优化问题时的预测与决策效果．通过对比其样本内性质及样本外性质发现，情景生成方法与投资组合优化模型对于中国股票市场来说，在预测与决策方面是非常有效的工具．其中矩匹配方法较其他方法能更好的反映市场的下跌趋势，多变量GARCH方法能更好的反映市场的上涨趋势．最后，列出了投资组合优化问题研究中有待进一步研究的几个问题．
[Abstract]:As a core subject of modern finance , the optimization problem of portfolio optimization focuses on how to make rational allocation and selection of financial assets under uncertain circumstances , so as to realize the equilibrium between yield maximization and risk minimization . In 1952 , U.S . economist HarryM . markwitz published " PortfolioSelection " in the journal of Finance Journal , and proposed the mean - variance portfolio selection theory . With the development of modern mathematics method and the application of mathematical method to study the financial mathematics of financial economy , the modern financial investment theory begins to get rid of the state of purely empirical operation and simple descriptive study . It has entered the advanced stage of quantitative analysis and provides guidance for investors to make investment decision . The rapid development of the world economy , the financial crisis and the frequent fluctuation of the market , the capital market of our country has been developed after the reform and opening up , but it is not too perfect and mature , so that the investors face more and more complex financial investment decision - making theories and practical problems , and the research on the optimization of investment portfolio is more and more important theoretical and practical significance .

This paper carries out the research work from the following three aspects : one is the optimization problem of portfolio optimization with base constraint , the second is the dynamic portfolio optimization problem with transaction cost , and the third is the comparison of the scenario production method of the investment portfolio stochastic optimization model . The main work is as follows :

1 . Artificial Bee Colony Algorithm is a new swarm intelligence algorithm proposed in recent years , which is more excellent in solving the problem of multi - modal high - dimensional function optimization . Considering the advantage of artificial swarm algorithm , an optimization model of portfolio optimization with radix constraint is studied by means of artificial swarm algorithm . Through numerical experiments , it can be found that the artificial swarm optimization algorithm is superior to other intelligent optimization algorithms when solving this problem .

2 . Aiming at the optimization problem of portfolio optimization with radix constraint , an improved artificial swarm optimization algorithm is proposed . In the algorithm , the Deb selection strategy is used to make the optimal solution satisfy the constraint condition , and a new search strategy is introduced to improve the convergence speed of the algorithm ;
At the same time , the bolzmann selection probabilities are used to maintain the population diversity and prevent the early maturity of the algorithm . Through the numerical experiments on the test problem , it is shown that using the algorithm can obtain better investment strategy and effectively disperse the portfolio risk , and show that the algorithm is fast and effective for solving the problem of portfolio optimization .

3 . A multi - stage mean - variance portfolio optimization problem with fixed transaction costs and proportional transaction costs is studied . Using the discrete - time dynamic programming method , the indirect utility function , the non - transaction region boundary and the analytic solution of the effective frontier are given , and the long - term optimal investment strategy of investors is determined . The solution process of the problem is described by numerical tests , and the influence of transaction cost on the effective frontier is explained .

4 . The optimal problem of mean - variance portfolio optimization with fixed transaction cost and proportional transaction cost is studied under the continuous time situation . By using the dynamic programming method , the Hamilton - BI - Bellman equation of the original problem is derived , and the explicit solution of the equation is obtained . Therefore , the optimal investment strategy and effective frontier expression of the original mean - variance problem are derived . The numerical test gives the effect of the change of transaction cost on the transaction area and effective frontier , and illustrates the feasibility and effectiveness of the method .

5 . The forecasting and decision - making effect of four scenarios generation method in solving the problem of portfolio optimization is studied . By comparing the intra - sample properties and the out - of - sample properties , the scenario - generating method and portfolio optimization model are very effective in forecasting and decision - making for Chinese stock market . Among them , the moment matching method can better reflect the market ' s declining trend compared with other methods , and the multi - variable forecasting method can better reflect the rising trend of the market .

Finally , several problems to be studied in the research of portfolio optimization are listed .
【学位授予单位】：西安电子科技大学
【学位级别】：博士
【学位授予年份】：2012
【分类号】：F224;F830.59

【引证文献】