基于不确定风险偏好系数与不确定效用函数的投资决策方法及应用

Investment Decision-Making Methods and Applications Based on Uncertain Risk Preference Coefficient and Uncertain Utility Function

摘要: 在投资决策中，风险偏好是影响投资者行为的关键因素，决定了资产配置和风险管理策略的选择，直接影响投资者决策。风险偏好一般可以分为风险厌恶、风险中性和风险爱好三类，风险偏好系数是衡量风险偏好的重要指标。效用函数可以量化投资者对不同投资组合的偏好，可通过效用函数将投资者目标和风险偏好参数化，从而建立可量化的决策模型，为投资决策提供基于效用最大化的结构化框架。不确定风险偏好系数引入了不确定变量，以量化投资者在不确定环境下的风险偏好变化，不确定效用函数将效用函数与不确定变量相结合，可用于不确定环境下投资决策方法的构建。但已有基于不确定效用函数的投资决策方法很少涉及投资者的风险偏好，也未考虑如何确定不确定风险偏好系数。基于此，本文给出了两类不确定风险偏好系数的确定方法，通过不确定效用函数期望、不确定效用函数方差与两类不确定风险偏好系数相结合，构建了两种基于不确定风险偏好系数与不确定效用函数的投资决策方法。本文通过多个数值算例验证了所提出的两种不确定投资决策方法的有效性与可行性。最后通过河北工程大学合同节水管理的实际案例进一步验证了所构建的两种基于不确定风险偏好系数与不确定效用函数的投资决策方法的实用性与应用价值。

Abstract: In investment decision-making, risk preference is a key factor influencing investors’ behavior, determining the choice of asset allocation and risk management strategies, and directly affecting investors’ decisions. Risk preference can generally be classified into three categories: risk-aversion, risk-neutral, and risk-seeking. The risk preference coefficient serves as an important indicator for measuring risk preference. The utility function can quantify investors’ preferences for different investment portfolios. By parameterizing investors’ objectives and risk preferences through the utility function, quantifiable decision-making models can be established, providing a structured framework for investment decisions based on utility maximization. The uncertain utility function, which combines the utility function with uncertain variables, can be used to construct methods for investment decisions under an uncertain environment. However, existing investment decision-making methods based on the uncertain utility function rarely involve investors’ risk preferences. Moreover, the methods involving risk preferences do not consider how to determine the uncertain risk preference coefficients. Based on this, this paper proposes two types of uncertain risk preference coefficient determination methods. By combining the expectation and the variance of the uncertain utility function and two types of uncertain risk preference coefficient, two investment decision-making methods based on the uncertain risk preference coefficient and the uncertain utility function are constructed. The effectiveness and feasibility of the two proposed uncertain investment decision-making methods are validated through multiple numerical examples. Finally, their practicality and applicability are further demonstrated via a practical application of a water saving management contract in Hebei University of Engineering.