摩擦市场下模糊增强型跟踪指数投资组合选择

发布时间：2018-03-02 19:38

本文选题：模糊数　切入点：跟踪误差　出处：《湖南大学》2013年硕士论文　论文类型：学位论文

【摘要】：在现代金融学里，基于随机不确定性对投资组合选择问题的理论研究已经发展到相当成熟的地步，然而证券市场中的不确定性大多表现为模糊不确定性，而证券市场的模糊性在以往的理论研究中往往被忽略，因此，基于模糊不确定性对投资组合选择问题的研究在理论和实践中都将具有非常重要和深远的意义。本文将模糊数理论与指数化投资理论相结合，在摩擦市场下，，构建了三种基于增强型跟踪指数模型的模糊投资组合选择模型。本文的模型对于金融市场中的摩擦因素只考虑了与交易数量成比例的交易费用。本文采用极大极小半绝对偏差跟踪指数误差来度量风险，并使它达到最小化得到跟踪指数投资组合模型。考虑到现实市场中的卖空限制、交易费用以及投资者对于投资组合期望收益的约束条件，即投资者对投资组合的收益有个最低的收益要求，从而得到增强型跟踪指数模型。本文首先把流动性引进来，把投资组合的流动性看作模糊数，于是得到第一个模型—带有模糊流动性约束的增强型跟踪指数投资组合模型。由于投资者对投资组合期望收益的满意水平以及跟踪误差的承受水平是不确定和模糊的，因此，我们把这些目标水平看作半梯形模糊隶属函数，以此来衡量投资者的满意程度，于是构建了基于模糊决策的增强型跟踪指数投资组合选择模型。接着，本文在考虑到投资者对跟踪指数误差、投资组合期望收益和流动性这三个目标的情况下，用对数型隶属函数分别来描述投资者对这三个目标的满意程度，继而构建了多目标的模糊增强型跟踪指数模型。最后，本文选取沪深300指数作为跟踪标的指数，选取沪深300指数成份股作为投资目标进行实证分析，通过变化隶属函数的参数值来尽可能准确地描述投资者对目标水平的满意程度，最后得到不同参数下投资者的投资组合。
[Abstract]:In modern finance, the theoretical research on portfolio selection based on stochastic uncertainty has developed to a rather mature stage, but the uncertainty in the securities market is mostly fuzzy uncertainty. However, the fuzziness of the securities market is often ignored in the previous theoretical studies. Therefore, the study of portfolio selection based on fuzzy uncertainty will be of great significance in both theory and practice. In this paper, the fuzzy number theory and the indexed investment theory are combined in the friction market. Three fuzzy portfolio selection models based on the enhanced tracking index model are constructed. In this paper, only the transaction costs proportional to the number of transactions are considered for the friction factors in the financial market. Small absolute deviations track exponential errors to measure risk, Considering the short selling restrictions, transaction costs and the constraints of investors on the expected return of the portfolio, the model is minimized to obtain the tracking index portfolio model. That is, the investors have a minimum return requirement on the return of the investment portfolio, thus an enhanced tracking index model is obtained. In this paper, the liquidity of the portfolio is first introduced, and the liquidity of the portfolio is regarded as a fuzzy number. The first model, an enhanced tracking index portfolio model with fuzzy liquidity constraints, is obtained. Since the investors' satisfaction with the expected return of the portfolio and the tolerance level of the tracking error are uncertain and fuzzy, We regard these target levels as semi-trapezoidal fuzzy membership functions to measure investor satisfaction, so we construct an enhanced tracking index portfolio selection model based on fuzzy decision. In this paper, the logarithmic membership function is used to describe the degree of satisfaction of investors with the three objectives of tracking the index error, the expected return of the investment portfolio and the liquidity, and the logarithmic membership function is used to describe the degree of satisfaction of the three objectives. Then the fuzzy enhanced tracking index model of multi-targets is constructed. Finally, this paper selects the Shanghai and Shenzhen 300 index as the tracking target index, and selects the Shanghai and Shenzhen 300 index component stock as the investment target to carry on the empirical analysis. By changing the parameter value of the membership function, the degree of satisfaction of the investor to the target level is described as accurately as possible. Finally, the portfolio of the investor under different parameters is obtained.
【学位授予单位】：湖南大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.91;F224

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