考虑投资者主观因素的模糊随机投资组合选择模型

发布时间：2018-01-04 07:06

本文关键词：考虑投资者主观因素的模糊随机投资组合选择模型　出处：《华南理工大学》2016年博士论文　论文类型：学位论文

【摘要】：当今投资组合理论形成了两大分支:一支是以马克维茨的投资组合选择模型为基石的资产配置方法,依据概率论用纯数量化方法度量各资产的收益和风险。然而,马氏模型的假设条件极其苛刻,其中最为核心且遭受非议最多的是有效市场和理性人假设。随着证券市场的不断发展,许多实证研究表明,投资者往往是有限理性的,证券市场也不总是有效的,人的心理和行为等因素对投资决策的作用不容忽视。这引发了科研工作者对行为的关注,产生了行为金融学,相应地发展起投资组合理论的另一个重要分支——行为投资组合理论。行为投资组合主要通过分析金融市场主体在市场行为中的偏差和信念来寻求不同市场主体在不同环境下的经验理论及决策行为特征,力求建立一种能正确反映市场主体实际决策行为和市场运行状况的描述性模型。如何运用经典投资组合理论的量化思想,将行为投资组合中市场的非有效性和投资者的有限理性进行量化,并将市场上实际存在的模糊不确定性和随机不确定性,以及投资者的心理和行为偏差反映到经典的投资组合选择模型中,是解决问题的关键,也是客观、准确、有效地构建投资组合选择策略的重要基础工作。本学位论文综合考虑了投资者的理性和非理性及不完全理性、市场的有效性和非有效性及不完全有效性,利用模糊随机理论建立投资组合选择的一系列模型,模型均假设收益率为模糊随机变量,且通过将模糊随机不确定问题合理转化为清晰系数的规划问题,最大限度地降低了决策信息的损失。因此,提出的模型能够帮助投资者在模糊和随机双重不确定环境下做出多元化的投资组合选择决策。在考虑投资者的个人偏好和心理偏差(包括投资者的乐悲观度、理性水平、情绪水平和风险偏好)等主观因素影响的基础上,我们进一步研究了带有各种约束条件的投资组合选择模型。如考虑最小交易手数、最小投资量限制、是否允许借贷无风险资产、是否允许买空、卖空及总投资资金金额限制等客观约束条件。最后将模型应用于现实的金融市场,检验其有效性和稳定性。本文主要创新点包括如下几个方面:(1)提出了模糊随机变量的清晰数字特征的概念;基于清晰数字特征建立了模糊随机投资组合均值-方差模型。结合模糊可能性理论和概率随机理论中数字特征的优势,定义了相应的模糊随机变量的数字特征,包括模糊随机可能性均值、模糊随机可能性方差和模糊随机可能性协方差等。解决了模糊随机不确定变量的期望值模糊不清给决策带来的困难;弥补了已有的模糊随机变量的方差和协方差不能清晰反映出模糊和随机两种不确定性下的离散度和相关性的不足。基于模糊随机变量的清晰数字特征,假设收益率为模糊随机变量,建立了风险资产的投资组合选择均值-方差模型,并通过一个投资实例说明了模型的有效性及较markowitz均值-方差模型的优越性。(2)提出了与模糊随机变量的λ期望相匹配的λ方差和λ协方差的概念;基于λ期望和λ方差建立了收益偏好和风险偏好相匹配的模糊随机投资组合λ均值-λ方差模型。现有的投资组合模型多是单独考察投资者对收益率的偏好或者单独考察投资者对风险的偏好。客观上,收益和风险是相互匹配的,即高收益高风险,低收益低风险。因此有必要在模型中考虑收益和风险相匹配的情况,以便投资者根据模型提供的结果做出客观理性的投资决策。基于λ权重均值的概念,为模糊随机变量定义了一种λ权重方差和λ权重协方差,进而获得了与λ权重均值相匹配的方差风险函数。基于λ均值和λ方差建立了收益风险相匹配的模糊随机投资组合模型。进一步考虑到投资者通常为了获得更高的风险回报,会通过借入无风险资产投资于风险资产组合,模型还讨论了允许借入无风险资产的情况。(3)量化了证券市场非有效造成的收益率的模糊不确定性和随机不确定性,量化了有限理性的投资者的乐悲观度和心理偏差给收益率带来的影响,从市场非有效和投资者有限理性的角度对模糊随机资产收益率做出了详细的金融解释。提出了模糊随机变量的(λ,γ)期望的概念;基于(λ,γ)期望建立了带有投资者乐悲观度、心理偏差和一系列现实约束的模糊随机投资组合选择模型。考虑到大多数投资者都是不完全理性的,在复杂的市场环境下,不同投资者具有各自不同的心理偏差,从资产的模糊随机收益中提取出投资者的主观因素信息,包括乐悲观度λ和可能性水平γ。详细分析了投资者的这些心理偏差对投资组合有效前沿的影响,发现具有不同心理偏差的投资者会选择不同的投资组合有效前沿。实证分析表明乐悲观度参数λ和可能性水平参数γ能够正确反映投资者的心理偏差,以及对决策结果产生的影响。在允许贷出无风险资产的情况下,将一系列现实约束条件加入到模糊随机模型中,做了进一步的分析和研究。结果表明,提出的模型由于综合了模糊和随机双重不确定性因素的影响,能够充分考虑到证券市场客观的现实约束和投资者主观的心理偏差,使得模型在市场不完全有效,投资者有限理性的情况下,比已有的概率论模型和模糊模型更加实用有效。(4)提出了模糊随机变量的(λ,γ,s)期望的概念;基于(λ,γ,s)期望,建立了带有投资者乐悲观度、风险偏好和心理偏差的模糊随机投资组合(λ,γ,s)均值-标准差模型。基于概率论和最优化理论的投资组合选择问题的研究大多遵循预期效用理论,而效用理论假设理性投资者都是风险厌恶的。但由于投资者心理存在着系统性偏差,使得风险厌恶并不总是成立。因此,不能将投资者的行为统一描述为风险厌恶或风险寻求,需要建立具有不同风险态度的投资组合选择模型。在前文基础上,提出了带有多种主观度参数的模糊随机期望收益率函数,并借助于模糊随机均值-标准差方法开发了一种模糊随机投资组合模型,解决了行为金融中不同投资者的风险偏好、不同乐悲观度、不同心理偏差程度和不同情绪水平的投资者的投资组合选择问题。
[Abstract]:The portfolio theory has formed two major clades: one is the asset allocation method to Markowitz's portfolio selection model based on probability theory as the cornerstone, with pure quantitative method to measure the asset's return and risk. However, assumption of Markov model is extremely demanding, the most important and the most criticism is effective the market and the assumption of rational people suffer. With the continuous development of the securities market, many empirical studies show that investors are limited rational, the stock market is not always effective, people's psychological and behavioral factors on investment decisions can not be ignored. This led researchers focus on behavior, behavioral finance has been produced accordingly, the development of another important branch of portfolio theory, behavioral portfolio theory, behavioral portfolio mainly through the financial market analysis in the market behavior Experience theory and decision-making behavior bias and belief for different market players in different environment, and strive to establish a correctly reflect the behavior and operation of the market situation the main body of the market decision-making. How to use the quantitative descriptive model of classic portfolio theory thinking, the limited rationality and effectiveness of non market investors investment behavior in combination are quantified, and the fuzzy real market uncertainty and random uncertainty, as well as the psychological and behavioral biases of investors to reflect the classical portfolio selection model, is the key to solve the problem is also an objective, accurate, basic work effectively to build a portfolio selection strategy in this thesis. Considering the investor's rational and non rational and irrational, the market validity and the validity and effectiveness of the use of incomplete, fuzzy A series of random model theory to establish the portfolio selection model, assume that the return is fuzzy random variable, and the fuzzy stochastic uncertain problem into a programming problem with rational coefficients, to minimize the loss of decision-making information. Therefore, the proposed model can help investors in the fuzzy and random double uncertain environment make a diversified portfolio selection decision. In consideration of personal preference and psychological deviation of investors (including investors optimistic and pessimistic, rational level, emotional level and risk preference) and other subjective factors influence, we further study with various constraints such as the portfolio selection model. Considering the minimum trade size the minimum amount of investment restrictions, whether to allow the borrowing of risk-free assets, whether short selling, short selling and the total investment amount limit and other objective constraints. Finally, the model is applied to the reality of the financial market, to test its effectiveness and stability. The innovations of this paper are as follows: (1) put forward the concept of the digital characteristics of fuzzy random variables; fuzzy random portfolio mean variance model is established based on the characteristics of clear digital. Combined with digital stochastic theory and fuzzy probability theory and the probability of feature advantages, defines the digital characteristics of fuzzy random variables corresponding, including fuzzy random probability fuzzy random mean value, variance and probability fuzzy random possibility covariance etc. to solve the fuzzy random variables of uncertain expectations for the decision blurred difficulties; the fuzzy random variable variance and covariance cannot clearly reflect the fuzzy and random two kinds of uncertainty of the discrete degree and correlation. Based on fuzzy random variables. Clear digital characteristics, assumption of return is fuzzy random variable, select the mean variance model to establish a risk asset portfolio, and the effectiveness of the model and compared with the Markowitz mean variance model is illustrated by an example of investment. (2) proposed the concept of a match with the expectation of fuzzy random variables. Lambda lambda variance and covariance; fuzzy random portfolio mean variance model of lambda lambda income and risk preferences to match the expectation and variance based on lambda lambda established. Most of the existing portfolio model separately examine the preference for yield or separately review the investor appetite for risk. Objectively, income and risk are mutually matched, namely high income high risk, low return and low risk. Therefore it is necessary to consider the benefits and risks of matching in the model, so as to provide investors according to the model results to make the guest The concept of rational investment decisions. Concepts of a weight value based on the definition of a lambda lambda weight weight variance and covariance for fuzzy random variables, and then get the variance risk function matching with weight value. The lambda fuzzy stochastic model for portfolio investment income risk to match the mean and variance of lambda lambda based on further. Considering that investors usually in order to obtain higher returns by borrowing the risk-free asset investment portfolio risk model is also discussed, allowed to borrow the risk-free asset. (3) the stock market rate of return caused by the non effective fuzzy uncertainty and random uncertainty quantification, quantification and optimistic and pessimistic psychological deviation of limited rational investors rate to the impact of income, make a detailed financial income of fuzzy stochastic asset ratio from the non effective market and investors in the perspective of bounded rationality Interpretation is proposed. The fuzzy random variables (x, y) based on the concept of expectation; (x, y) was established with the optimistic and pessimistic expectations of investors, fuzzy random portfolio selection model of psychological deviation and a series of practical constraints. Considering that most investors are not fully rational, in the complex market environment. Next, different investors have different psychological deviation, the extraction of information from the subjective factors of investors fuzzy random profit assets, including the optimistic and pessimistic degree and possibility. The gamma lambda level affect the investor's psychological deviation of the portfolio efficient frontier analysis found to have different psychological deviation of investors will be different investment choices efficient frontier. The empirical analysis shows that the optimistic and pessimistic parameter lambda and possibility level parameter can reflect the psychological bias of investors, and the influence on the decision results produced in. Allowed to lend a risk-free asset in the case, a series of practical constraints into fuzzy stochastic model, do further analysis and research. The results show that the proposed model due to the combined influence of fuzzy and random uncertainty factors, can give full consideration to the securities market objective reality and subjective constraints investor psychological bias that makes the model in the market is not fully effective, investors in the condition of limited rationality, model and fuzzy model is more practical and efficient than the existing probability. (4) proposed the fuzzy random variables (x, y, s) based on the concept of expectation; (x, y, s) was established with the expectations of investors the optimistic and pessimistic, fuzzy random portfolio risk preference and psychological deviation (x, y, s) the mean standard deviation model. Research on the probability theory and the optimization theory of portfolio selection problem mostly follow the expected utility theory based on The utility theory, the hypothesis of rational investors are risk averse investors. But because there are systematic psychological deviation, the risk aversion is not always true. Therefore, the behavior of investors will not seek for the unified description of risk aversion or risk, need to establish with different risk attitude of the portfolio selection model. Based on the above analysis, put forward with a variety of subjective parameter of fuzzy random expected yield function, and by using fuzzy random mean standard deviation method developed a fuzzy random portfolio model, solve the risk preference of different investors in different financial behavior, optimistic and pessimistic, different psychological deviation degree and investors with different levels of emotional investment portfolio the problem.

【学位授予单位】：华南理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：F224;F830.59

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