基于信息熵的风险决策模型及其在投资决策中的应用

Virtually all economic and technological decisions involve risk or uncertainty and their measures. Being uniqueness as the measure of uncertainty, information entropy is introduced into decision-making under risk. Thus, it is essential to study and develop information entropy based decision-making model under risk and its applications. This project aims to develop the approach both on measure of risk and decision-making model based on combined form of information entropy and expected utility, and then establish a descriptive model of decision-making under risk in accordance with decision-makers’ real behavior and a rational normative decision making model. We also investigate to establish the axiomatic decision-making model under risk based on information entropy. Furthermore, we explore the relationship between information entropy based risk measure and ordinal measure of risk, and moreover information entropy based decision making model and stochastic dominance criterion. With the background of portfolio optimization, financial risk management etc., we investigate to establish information entropy based investment decision and portfolio optimization model, and apply them to the stock selection and portfolio optimization and other financial risk management. The research of the project will be of a great significant in using advantage of information entropy to measure uncertainty and establishing the new descriptive and normative model theoretically. The research results can be applied to portfolio optimization and risk analysis to China’s stock market.

几乎所有经济或技术决策都涉及风险或不确定性及其度量，由于信息熵度量不确定性有独特优势，因此将信息熵引入到风险决策研究中，发展基于信息熵的风险决策模型及其应用很有必要。本项目旨在发展和完善将信息熵和期望效用理论结合起来的风险度量与决策模型和方法，构建更加符合决策者实际决策行为的风险决策的描述性模型和合乎理性的规范化模型；探求建立满足公理化体系的基于信息熵的风险决策模型和方法；研究基于信息熵的风险行动的风险度量与序型度量之间的关系，研究基于信息熵的风险决策模型同随机占优方法之间的关系等。以股票投资组合优化和金融风险管理等风险决策为背景，研究建立基于信息熵的投资决策和组合优化模型，应用于股票投资选择和组合优化及其它金融风险管理中。本项目的研究意义可以利用信息熵度量不确定性的优势，在理论上建立更加科学的风险决策的描述性模型和规范化模型，研究成果用于我国投资组合优化和风险管理实际。

几乎所有经济或技术决策都涉及风险或不确定性及其度量，由于信息熵度量不确定性有独特优势，因此将信息熵引入到风险决策研究中，发展基于信息熵的风险决策模型及其应用很有必要。本项目旨在发展和完善将信息熵和期望效用理论结合起来的风险度量与决策模型和方法，构建更加符合决策者实际决策行为的风险决策的描述性模型和合乎理性的规范化模型；探求建立满足公理化体系的基于信息熵的风险决策模型和方法。本研究建立了基于期望效用和信息熵的风险行动金融资产的风险度量方法，由此对投资金融资产风险进行排序；提出了基金评级方法并研究该方法基金评级的预测能力，得到利用该方法选择基金投资组合绩效更优的稳健结论；研究建立了基于期望效用和信息熵的风险行动的决策模型，并利用该决策模型进行股票选择投资，得到组合优化的结果；研究建立了基于期望效用和信息熵的证券投资组合风险度量模型及其在证券投资组合优化决策中的应用，可以提高投资组合业绩降低风险。.本项目的研究意义在于利用期望效用和信息熵的优势，在理论上建立了基于期望效用和信息熵金融资产的风险度量和决策的规范化模型，研究成果用于基金评级、股票投资选择，以及投资组合的优化等风险管理实际。