寻求现实多阶段投资组合选择问题时间相容最优投资策略的高性能算法

Medium and long term investment problems in practice can be described as multi-stage portfolio selection problems. Since they did not coordinate key issues such as the random investment environment description, the risk measure selection and the algorithm design, current algorithms can not solve real multi-stage portfolio selection problems because of the "curse of dimensionality". This problem has become a crucial problem to be solved urgently and has attracted scholars in fields such as financial engineering and operations research. This project proposes a new two-level framework for describing the market stochastic evolution, which have several unique advantages, and design time consistent multi-period risk measures, which are easy to compute, through new ways like establishing a generic composite form for multi-period risk measures. Our new random framework and time consistent multi-period risk measures overcome the fatal weakness of existing random framework and risk measures: they can only satisfy a single desirable property. By introducing proper constraints, we construct multi-stage portfolio selection models which can flexibly reflect various market frictions and can avoid arbitrage opportunity. By sufficiently utilizing modern optimization techniques such as stochastic optimization, conic program, and skillfully breaking through several technical bottlenecks restricting problem solution, we design several high performance algorithms which can solve realistic multi-stage investment decision problems. This project will solve the real solvability problem of medium and long term investment problems, and eliminate the gap between the current theoretical research and practical application. Our research will provide scientific support for the development of domestic mutual fund market, the management of domestic financial markets and the establishment of relevant investment laws and regulations.

实际的中长期投资问题均可表述为多阶段投资组合选择问题。因未能协调解决随机环境描述、风险度量选择与算法设计等关键问题，导致现有算法因"维数灾难"无法求解实际中的多阶段投资组合选择问题，这已成为亟待解决的难点问题而倍受金融工程、运筹学等领域学者的关注。本项目通过提出有多个独特优势的描述市场随机演变的双层框架、建立风险度量的一般复合模式等新途径来设计易于计算的时间相容的多期风险度量来克服现有描述框架与风险度量仅满足某单一要求的弱点；引进适当的约束条件，构建可灵活兼顾不同市场摩擦、且可规避套利机会的多阶段投资组合选择模型；综合运用随机优化、锥规划等近现代优化技术，巧妙突破制约问题求解的多个技术瓶颈，设计数个高性能算法，并用于求解实际的多阶段投资决策问题。项目研究将尝试解决中长期投资问题的现实可解性问题，消除理论研究与实际应用的差距，并为我国基金市场的发展、金融市场管理和相关法规的制定提供科学依据。

能按研究计划开展工作，很好地完成了预期研究任务。所取得的主要研究成果如下：我们首先总结了多期风险度量应满足的基本性质, 并将已有文献中出现的多期风险度量按其构造方式分为三类；基于乘积空间设计出了一个“两层”框架来恰当描述多阶段投资问题中不确定信息随时间随机动态变化的相依关系；基于所提出的随机框架，通过复合模式等技巧，我们相继设计了近十种满足凸性和时间相容性等的具有良好特性且易于计算的多阶段风险度量；对凸风险度量和一致性风险度量的关系进行了系统探讨，由此设计了数个新型的一致性风险度量，探讨了它们在多阶段情形的拓广问题；对于所提出的每种新型（多期）风险度量，我们均构建了相应的兼顾不同市场摩擦且可规避套利机会的（多阶段）投资组合选择优化模型，通过寻求其解析最优解，或设计高性能算法并展开实证研究论证了新度量和投资组合模型的实用性与有效性；为了更好地反映实际的市场环境，并能寻求到满足时间相容性的最优投资策略，我们就现有多期投资组合选择模型的修正、现实多阶段投资组合选择模型的构建、度量的时间相容性与策略的时间相容性概念的拓广等问题展开了一系列研究，使得我们可以寻求到实际中复杂多期投资问题时间相容的最优投资策略；作为本项目的理论基础与算法基础，我们还对几种多阶段随机规划问题的稳定性进行了系统分析，同时就情景树生成或约简的有效算法，特别是这些新算法在求解现实多阶段投资组合选择优化问题中的应用进行了研究，以使我们能克服多个技术瓶颈，快速寻求到可规避套利机会的时间相容的最优投资策略；最后，对与本项目相关的超效益模型的不可行性问题，固定费用（资源）分配问题，多属性决策问题等复杂决策问题进行了研究.