模糊投资组合优化及应用研究

发布时间：2018-01-04 04:32

本文关键词：模糊投资组合优化及应用研究　出处：《哈尔滨工业大学》2014年硕士论文　论文类型：学位论文

【摘要】：金融市场充满了不确定性，受到诸如：国内外经济形式、经济政策、自身运行规律、气候、灾害等各种因素的影响，这使得投资者获得的数据具有非常大的不确定性。对投资组合选择问题中的随机不确定性问题，研究者已经通过应用统计学中的均值、方差的方法加以了解决，在实践中也发挥了重要的作用。然而，现实世界中，，尤其是在证券市场上，数据的不确定性也表现为模糊性，模糊现象大量存在。传统的投资组合模型无论怎么变，都只用了统计学中的期望、方差解决了金融市场的随机性问题，而不确定性中的模糊性却没有得到解决，因此研究模糊环境下的投资组合决策正好可以解决这一问题。目前已经有不少学者对模糊条件下的投资组合进行了研究，运用不同的理论将模糊性引入投资组合模型中，发现模糊性对投资组合可能会产生影响。本文在系统性的整理这些研究成果的同时，分别运用模糊决策理论、模糊可能性理论、区间数理论，从对模糊性衡量的不同角度，研究了模糊决策投资组合、模糊可能性投资组合、区间数投资组合，并通过放宽市场无摩擦约束、改变决策变量等方式将这些模型进行了进一步的优化。本文还对这些模型通过变量替换和加权的方法转化成线性模型，并分别运用上证50指数中的样本进行了实证研究，研究的结果表明，考虑数据模糊性和市场摩擦的投资组合实用性更强，并且优化后的模型能最大限度的反映出投资者的意愿，灵活性较强、应用范围更广。总之，在理论上能拓展传统投资组合的研究思路，实践上能起到很好的指导价值。
[Abstract]:The financial market is full of uncertainty, which is influenced by many factors, such as domestic and foreign economic forms, economic policies, its own operating rules, climate, disasters and so on. This makes the data obtained by investors have great uncertainty. The stochastic uncertainty in portfolio selection problem has been solved by applying the mean and variance methods in statistics. It also plays an important role in practice. However, in the real world, especially in the securities market, the uncertainty of data is also shown as fuzziness. The traditional portfolio model, no matter how it changes, only uses the expectation in statistics, the variance solves the randomness of financial market, but the ambiguity in uncertainty is not solved. Therefore, the study of portfolio decision in fuzzy environment can solve this problem. At present, many scholars have carried on the research to the investment portfolio under the fuzzy condition, using different theories to introduce the fuzziness into the portfolio model. Find that fuzziness may have an impact on the portfolio. This paper systematically collates these research results, respectively using the fuzzy decision theory, fuzzy possibility theory, interval number theory. From different angles of fuzziness measurement, this paper studies the fuzzy decision portfolio, fuzzy possibility portfolio, interval number portfolio, and relax the market non-friction constraints. These models are further optimized by changing the decision variables. This paper also transforms these models into linear models by means of variable substitution and weighting, and carries out empirical research using the samples in the Shanghai Stock Exchange 50 Index, the results of which show that. Considering the fuzziness of the data and market friction, the portfolio is more practical, and the optimized model can reflect the wishes of investors to the maximum extent, flexibility is stronger, the scope of application is wider. In theory can expand the traditional portfolio research ideas, in practice can play a good guiding value.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F830.91

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