基于混合熵的投资组合风险度量模型研究

发布时间：2018-06-30 03:42

本文选题：混合不确定性 + 模糊收益率　；参考：《大连理工大学》2013年硕士论文

【摘要】：经典投资组合理论中,用收益率的方差衡量投资组合的风险,其前提假设是收益率服从正态分布。这一前提与现实情况并不相符,证券收益的随机不确定性和模糊不确定性同时存在。因此,论文引入混合熵作为衡量证券的风险的指标。混合熵可以表示由概率不确定性和模糊不确定性的混合不确定性。在不考虑模糊因素时且收益服从正态分布时,混合熵与方差在衡量风险时等价；而在收益非正态分布以及考虑证券收益模糊性时,由于证券的最高和最低收益的影响,混合熵在风险度量时相对方差法更加合理。混合熵改进了方差度量时仅考虑证券收益随机性的缺陷,在证券风险衡量时更符合现实情况。采用混合熵衡量投资组合的风险时,由于不同证券之间的相关性时极其复杂,若忽略相关性建立线性规划求解将导致所选择的证券组合中证券数量仅为1或2,有悖投资组合分散风险的初衷。因此,论文在忽略证券之间相关性建立线性规划的同时加入了新的风险分散约束熵函数,作为对忽略证券相关性以及投资组合证券数量过少的补偿。利用matlab为计算工具,选取上证180指数中的十只证券进行算例计算,同时变换风险分散约束熵函数在多目标规划问题中的权重求解最优证券组合,可以明显发现,当风险分散约束熵函数的权重增加时,最优组合中的证券数量明显增加,组合的总风险相对稳定。
[Abstract]:In classical portfolio theory, the risk of portfolio is measured by the variance of return rate, and the premise is that the yield is assumed to be normal distribution. This premise does not accord with the real situation, and the stochastic uncertainty and fuzzy uncertainty of the securities return exist simultaneously. Therefore, the mixed entropy is introduced to measure the risk of securities. Mixed entropy can represent the mixed uncertainty by probability uncertainty and fuzzy uncertainty. When the fuzzy factor is not considered and the return service is normal distribution, the mixed entropy and variance are equivalent in measuring the risk, while in the non-normal distribution of the income and the fuzziness of the income of the securities, because of the influence of the highest and the lowest return of the securities, The method of relative variance is more reasonable in risk measurement. The mixed entropy improves the variance measurement by considering only the randomness of security returns, which is more in line with the reality in the measurement of securities risk. When using mixed entropy to measure the risk of a portfolio, because the correlation between different securities is extremely complex, If the linear programming solution is established to ignore the correlation, the number of securities in the selected portfolio will be only 1 or 2, which is contrary to the original intention of portfolio diversification. Therefore, a new risk dispersion constraint entropy function is added to the linear programming to compensate for the neglect of the correlation between securities and the small number of portfolio securities. By using matlab as a calculation tool, ten securities in the 180 index of Shanghai Stock Exchange are selected for calculation. At the same time, the optimal portfolio can be found by transforming the weight of the entropy function of risk dispersion constraint in the multi-objective programming problem to solve the optimal portfolio. When the weight of the entropy function increases, the number of securities in the optimal portfolio increases obviously, and the total risk of the portfolio is relatively stable.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.59

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