多期投资组合的优化分析及其鲁棒模型研究

发布时间：2018-06-01 00:32

本文选题：多期投资组合 + 随机规划　；参考：《山东大学》2013年硕士论文

【摘要】：本文研究的对象是多期投资组合问题,由于投资者在投资时不可能预知资产未来的收益率,所以本文将资产收益率看作随机量建立随机规划模型,并用随机规划对偶理论和鲁棒优化方法对模型进行处理。本文首先对多期投资组合问题进行优化分析,研究了在有若干资产供选择进行多期投资时,将初始资金投资到全部资产上做一个多期投资组合是否优于将初始资金分为若干部分任选几种资产做多个多期投资组合的问题。根据投资实践中投资分散的要求,本文向多期投资组合问题中加入资产分散约束,并构造了该问题的两阶段有补偿模型；然后以资产为虚拟的局中人构造了一个合作博弈问题,并定义了该合作博弈问题的支付函数；最后利用随机规划的对偶证明了该合作博弈存在核心分配,这说明了将初始资金投资到全部资产上做一个多期投资组合的确优于将初始资金分为若干部分各任选几种资产做多个多期投资组合。我们还通过一个简单的例子进一步阐述了这一点。在经典的Markowitz的均值方差模型中,期望收益的微小变化会对最优资产分配产生较大影响,即该模型缺乏稳健性。本文借鉴单期投资组合中稳健的定义,研究了稳健的多期投资组合问题,并且以方差衡量风险,在市场上只有风险资产且不限制卖空的前提下建立一个随机规划模型。传统的求解随机规划的方法往往需要知道随机量的概率分布,这一点很难实现,而且计算起来比较困难。鲁棒优化方法是研究不确定性问题的一种十分有效的方法。该方法不要求已知随机参数的概率分布而且计算简便。本文考虑了不同的不确定集,将一个随机线性约束等价的转化为线性约束或二阶锥约束,这样原问题可转化为一个二阶锥规划,使问题更易于处理。最后本文选取上海证券市场的股票进行算例分析,使用Matlab求解对应的二阶锥规划问题,验证了鲁棒优化方法的有效性。
[Abstract]:In this paper, the object of this study is a multi term portfolio problem. As investors can not predict the future yield of assets, this paper considers asset returns as random quantities to establish random programming models, and uses stochastic programming duality theory and robust optimization method to deal with the model.
In this paper, the problem of multi period portfolio is optimized, and the problem of whether the initial capital is invested in all assets is better than the initial fund is divided into several types of assets to be a multi period portfolio. The requirement of the decentralization of investment in the practice is to add the asset dispersion constraint to the multi term portfolio problem and construct the two stage compensation model for the problem. Then, a cooperative game problem is constructed for the people in the asset virtual Bureau, and the support function of the cooperative game problem is defined. Finally, the dual proof of the random programming is used. It is clear that there is a core allocation in the cooperative game, which shows that it is indeed better to invest the initial funds in a multi term portfolio than to divide the initial funds into a number of selected assets to be multiple and multi term portfolios. We also illustrate this point by a simple example.
In the mean variance model of the classical Markowitz, the small change in expected return will have a greater impact on the optimal asset allocation. That is, the model is lack of robustness. This paper studies the robust multi term portfolio problem for reference by the robust definition of the single phase portfolio, and measures the risk by variance, and the only risk assets in the market. A stochastic programming model is established without restricting short selling. The traditional method of solving random programming often needs to know the probability distribution of random quantities. This is difficult to realize, and it is difficult to calculate. The robust optimization method is a very effective method to study the uncertainty problem. The probability distribution of the number and the calculation are simple. In this paper, different uncertain sets are considered and the equivalent of a random linear constraint is converted into a linear constraint or two order cone constraint. So the original problem can be converted into a two order cone programming, making the problem more easy to deal with. Finally, the stock of the Shanghai stock market is selected for example analysis and use of Matla B solves the corresponding two order cone programming problem, and verifies the effectiveness of the robust optimization method.
【学位授予单位】：山东大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：O221.5;F832.48

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