稳健投资组合选择的并行最优化算法研究与实现

Robust portfolio optimization is one of the key techniques in quantitative investment management, and the practical applications of robust portfolio selection have strong demands for high-performance algorithms and implementations. In this project, we shall firstly model the practical portfolio selection problems reasonably based on the methodology of robust optimization, then study the effective algorithms to solve the optimization models, and finally explore and implement the parallel algorithms. Our research will focus on the parallel algorithms for (mixed-integer) second-order cone programming and ill-behaved nonconvex optimization problems arising in robust portfolio optimization. With the increasingly popular heterogeneous high-performance computing systems, we shall optimize the computational performance in multi levels and achieve the goals of almost real-time response to the calculations of robust portfolios, output the model toolbox, high-performance algorithmic library and solvers for robust portfolio selection. We shall scale the parallel computing to 1000 CPU cores and get the parallel efficiency over 60%. This project is motivated by the specific financial applications and combined with multiple disciplines. It targets the state-of-the-art of modern portfolio theory, and captures the practical computational bottlenecks. The innovations of our research lie in the following aspects: robust portfolio selection models, global parallel numerical algorithms for (mixed-integer) second-order cone programming, financial calculation in heterogeneous computing environment, and so on. Our research will promote the development of modern portfolio theory, the innovation of robust portfolio selection methods and the amalgamation of computational technology & the investment management practice. And this research also own great practical significance and long-term application value for expanding the industrial applications of high-performance computing and improving the investment management ability of financial investment institutions.

稳健投资组合选择是数量化投资管理领域中的一项关键技术,目前其在应用中亟需高性能算法与实现研究。本项目针对现实投资场景下的投资组合选择问题，基于稳健优化方法构建合理的最优化模型，结合模型结构设计高性能算法并研究其并行化策略；着重研究典型的（混合整数）二阶锥规划和病态非凸优化问题的并行算法；结合目前主流的高性能计算系统架构，利用并行计算技术多层级优化性能，实现对稳健投资组合计算的快速响应；产出具有自主知识产权的稳健投资组合选择模型工具集、算法库和求解器；实现千核级规模计算，并行效率逾60%。该研究由具体应用驱动，多学科渗透，瞄准了现代投资组合理论前沿，切中了具体应用瓶颈，在投资组合选择建模、（混合整数）二阶锥规划全局并行算法设计、异构环境下计算金融实现三方面将有创新。预期成果将促进相关学科理论发展、投资组合优化方法创新、高性能计算应用、以及计算技术与投资管理实践的融合，具有现实意义和应用价值。

稳健投资组合选择是数量化投资管理领域中的一项关键技术,目前其在应用中亟需高性能算法与实现研究。本项目针对现实投资场景下的投资组合选择问题，基于稳健优化方法构建出了合理的最优化模型，结合模型结构设计了高性能算法、研究了其并行化策略并进行了程序实现。.项目按计划执行，进展顺利，取得了多项研究成果：1）在稳健投资组合优化模型构建方面，基于可信性理论、模糊理论及分位数回归等方法，改进了传统的均值-方差模型，并且加入现实约束，使模型更贴近于市场实际状况；2）在稳健投资优化组合模型输入参数的确定方面，基于多因子模型和GARCH族模型等方法，对资产的收益率和波动率进行了研究，得到稳健投资组合模型所需要的输入；3）在稳健投资组合选择的并行算法与实现技术方面，针对不同的稳健投资组合模型，分别设计出了基于模糊模拟和遗传算法的混合智能求解算法、高效加速方法、基于MPI+OpenMP和MIC架构的并行模拟方法、基于SCIP和Bonmin构造的混合整数规划算法等一系列高性能并行算法。.项目组积极参加了国内外学术合作交流，在项目经费支持下，创办了“金融与计算论坛”(Finance and Computing Forum，FCF)，这是国内首个金融与计算交叉研究的特色品牌会议，有力推动了计算、金融及统计的学科交叉研究以及学界和业界的合作，形成了一定的影响力。.本项目研究由具体应用驱动，多学科渗透，瞄准了现代投资组合理论前沿，切中了具体应用瓶颈，在投资组合选择建模、并行算法设计、异构环境下计算金融三方面实现了创新，促进了相关学科理论发展以及计算技术与投资管理实践的融合，具有学科意义和应用价值。