基于模糊熵的贷款组合决策模型

发布时间：2018-05-07 16:08

本文选题：模糊变量 + 可信性理论　；参考：《山东师范大学》2014年硕士论文

【摘要】：在马柯维茨（Markowitz）经典的均值—方差理论中，把收益率假设成为服从正态分布，利用收益率的方差度量投资中的风险，但这个假设经常与现实情况不一样。我国商业银行的贷款收益率具有模糊不确定性，因此，我们把收益率假设成模糊变量，引入模糊熵和信息熵来度量贷款的风险程度。模糊熵具有描述信息不确定程度的性质。当我们把收益率考虑成随机变量且服从正态分布时，模糊熵与方差在度量风险方面是等价的；但是当考虑收益率为模糊变量且不服从正态分布时，受到贷款资金在不同收益下风险等级不同的影响，模糊熵在风险衡量方面比方差更加合理。模糊熵改进了方差依靠概率分布且计算复杂的缺陷，在度量贷款风险时更加符合实际情况。使用模糊熵度量贷款组合的风险时，因为不同的贷款项目之间会有复杂的相关性，所以如果忽视相关性构建贷款组合模型求解会使决策选择集中在一个或者某几个高收益的贷款项目中，与我们组合贷款的思想相违背。因此，为了解决这个小小的瑕疵，在模型中加入了分散风险的约束条件，从而弥补对忽视贷款项目间相关性以及贷款组合的组合数目过少的补偿缺陷。利用模糊模拟和遗传算法相结合的混合智能算法解决模型求解问题。该算法打破常规，使得求得最优解变为可能，，并验证了算法的可行性。
[Abstract]:In the classical mean-variance theory of Markowitz (Markowitz), the assumption of return is changed from normal distribution to measure the risk in investment with the variance of return, but this assumption is often different from the real situation. The loan yield of commercial banks in our country has fuzzy uncertainty. Therefore, we assume the rate of return as a fuzzy variable, and introduce fuzzy entropy and information entropy to measure the risk degree of loan. Fuzzy entropy has the property of describing the degree of uncertainty of information. When we consider the rate of return as a random variable and take it from the normal distribution, the fuzzy entropy and variance are equivalent in measuring risk, but when we consider the rate of return as a fuzzy variable and do not agree with the normal distribution, The fuzzy entropy is more reasonable than variance in risk measurement because of the different risk grade of loan funds under different income. Fuzzy entropy improves the defect that variance depends on probability distribution and computes complexity, which is more in line with the actual situation in measuring loan risk. When using fuzzy entropy to measure the risk of a loan portfolio, because of the complex correlation between different loan projects, Therefore, if we ignore the correlation and construct the loan portfolio model solution, the decision will be concentrated in one or several high-yield loan projects, which is contrary to our idea of portfolio loan. Therefore, in order to solve this small flaw, the constraint condition of decentralized risk is added to the model to compensate for ignoring the correlation between loan projects and the small number of loan portfolio. A hybrid intelligent algorithm, which combines fuzzy simulation and genetic algorithm, is used to solve the problem of model solving. The algorithm breaks the convention and makes it possible to find the optimal solution, and verifies the feasibility of the algorithm.
【学位授予单位】：山东师范大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F830.5

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