复杂不确定环境下鲁棒投资组合优化模型及决策研究

There frequently are manifold uncertainties in the security market, such as the randomness of future market trend and the fuzziness of future earnings. Furthermore, double uncertainty always appears in security market because of the interpenetration of these two uncertainties so that the investors always make decisions in such a complex environment. Thus, the project will take advantage of uncertainty theory to deal with resulting double uncertainty in security market. Based on the methodology of robust optimization, the project will consider portfolio selection problem with fuzzy random returns in the complex uncertain environment. This project will propose and develop a scientific method of obtaining robust investment strategies to cope with external disturbance by effectively incorporating historical data and the subjective experiences of experts. The main topics include: (1) to propose two kinds of robust portfolio optimization models incluing regret minimization and robust mean-risk models, and extend them to multi-period situation; (2) to enrich the proposed models to characterize the real investment environment by introducing more factors such as transaction cost, liquidity constraints and bankruptcy risk control; (3) to design efficient and effective hybrid intelligent algorithms to solve and analyze the propsoed models by integrating fuzzy random simulation, neural network and heuristics; (4) to apply the proposed models to model the asset-liability management problem in the insurance and demonstrate the necessity by employing these robust optimization models.

证券市场中往往并存着多种不确定性，如未来市场走向的随机性、证券未来收益的模糊性，以及它们相互渗透而形成的双重不确定性，从而使投资者总是在这样复杂的不确定环境下进行投资决策。鉴于此，本项目拟利用不确定理论处理证券市场中出现的双重不确定性，根据鲁棒优化的建模思想，研究复杂不确定环境下的投资组合选择问题，力求建立并发展一套能有效应对外界扰动并有效融合历史数据与专家主观经验进行稳健投资决策的科学方法。研究内容：（1）建立后悔度最小化和鲁棒均值-风险等两类鲁棒投资组合优化模型，并拓展至多期模型的形成与分析；（2）逐步引入交易成本、流动性约束、破产风险控制等市场机理因素，形成逐渐接近现实投资决策环境的鲁棒优化模型；（3）设计有效的集模糊随机模拟、神经元网络与启发式算法于一身的混合智能算法对模型进行求解与分析；（4）应用新模型解决保险中的资产负债管理等问题，并论证采用这些模型的必要性。

不确定性广泛存在于证券市场之中，从而使投资者总是在多重不确定性并存时的复杂环境下进行投资决策。本项目聚焦于主客观不确定性并存时的投资组合选择问题，使用不确定随机变量等混合变量刻画证券收益，综合运用投资组合理论、不确定理论及运筹学的相关理论进行建模分析，为复杂不确定环境下的投资组合选择问题构建了后悔度最小化、均值-风险型等多种优化模型，并拓展至多期问题、再调整问题等情形。在模型求解时，项目组首先对所构建模型进行理论分析，并在一定条件下将其转化为确定等价形式。对于不能转化成确定形式的模型，使用模拟技术估计相关参数或表达式，设计混合智能算法进行数值求解与分析。随着研究的深入和国内外同类研究的进展，本项目亦对相关的不确定性建模及决策问题进行了应用研究和深化。项目组成员在为期四年的研究中，共发表了19篇标注课题资助的SCI检索期刊论文，主要分布在国内外运筹学与管理科学及其他交叉学科领域的重要学术期刊上，并在Springer出版一部学术专著，参加了20余人次国内外学术会议，招收3名博士生和7名学术型硕士生。