关于模糊变量的多期投资组合优化模型

发布时间：2018-05-19 00:06

本文选题：模糊变量 + 投资组合优化　；参考：《兰州理工大学》2017年硕士论文

【摘要】：人们在投资中,考虑到要将风险分散,往往选择不同的投资项目进行投资;为了使投资的比重更加合适还需要对具体的投资资产做多元化的分配,伴随这个问题,证券投资组合理论应运而生。由于在投资市场中,人们的大众行为受思维和环境等因素的影响,而人的思维判断具有一定的模糊性以及经济现象本身所具有的复杂性使得现实金融市场具有不确定性和模糊性,传统的概率论方法下的投资组合模型已经不能满足现实市场的需求,理性的投资决策在满足风险收益均衡的同时还需要考虑很多标准。因此,模糊方法比概率方法更适合表达真正金融市场的不确定性。本文基于经典的均值-方差理论,模糊集的概念和可能性理论,运用模糊方法来表达金融市场中的不确定性。在满足投资者的最大收益和最小风险两个愿望水平的前提下,假设收益率为模糊变量,从而得到相应的模糊投资组合优化模型。由于现实生活中的投资市场是复杂的、移动的,在满足风险收益均衡的同时还考虑很多其他因素,例如:交易成本,多元化程度等。对于资产具有相同投资期限的情况,在假设收益率为模糊变量的条件下考虑变动市场的因素,建立了模糊投资组合优化模型;在假设收益率为历史收益率的线性组合模糊变量的条件下,建立了相应的模糊投资组合优化模型,并且均进行了实例验证,与传统的模型结果相对比,更符合现实的金融市场情况。对于资产具有不同投资期限的情况,假设资产的投资期限可能小于投资期数、也可能大于投资期数,分别得出了相应的财富表达式,并且给出了实例验证。
[Abstract]:In investment, people tend to invest in different investment projects in order to spread out the risks; to make the proportion of investment more appropriate, they also need to diversify the allocation of specific investment assets, along with this problem. Portfolio theory emerges as the times require. Because in the investment market, people's public behavior is influenced by factors such as thinking and environment, The fuzziness of human's thinking judgment and the complexity of economic phenomenon make the real financial market have uncertainty and fuzziness. The traditional portfolio model based on probability theory can not meet the needs of the real market. Rational investment decision can not only meet the risk and return equilibrium, but also need to consider a lot of criteria. Therefore, the fuzzy method is more suitable than the probability method to express the uncertainty of the real financial market. Based on the classical mean-variance theory, the concept of fuzzy set and the possibility theory, this paper uses the fuzzy method to express the uncertainty in the financial market. On the premise of satisfying the two desired levels of maximum return and minimum risk of investors, the fuzzy portfolio optimization model is obtained by assuming that the return rate is a fuzzy variable. Because the investment market in real life is complex and mobile, many other factors are considered, such as transaction cost, diversification degree and so on. For the case where the assets have the same investment term, the fuzzy portfolio optimization model is established under the assumption that the return rate is a fuzzy variable, and the factors of the changing market are considered. Under the condition that the return rate is assumed to be a linear portfolio fuzzy variable with historical rate of return, the corresponding fuzzy portfolio optimization model is established, and it is verified by examples, and compared with the results of the traditional model. More realistic financial market conditions. For the case where the assets have different investment periods, it is assumed that the investment period of the assets may be less than the investment period or the investment period may be larger than the investment period. The corresponding wealth expressions are obtained respectively, and an example is given to verify the results.
【学位授予单位】：兰州理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F832.5;O159

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