无风险控制的log-最优投资组合问题的一个黎曼几何随机算法  

An Riemannian Geometry Underlying Stochastic Algorithm for the Risk-free log-Optimal Portfolio Problem

作　　者：董承非[1] 黄建国[1] 

机构地区：[1]上海交通大学数学系,上海200240

出　　处：《华东理工大学学报（自然科学版）》2004年第1期103-106,共4页Journal of East China University of Science and Technology

摘　　要：无风险控制的log-最优投资组合问题是一个很有实际应用价值的计算金融问题,本文给出了求解该问题的一个内蕴的自然梯度随机算法。算法的内在优点是每步迭代所得近似结果都自动满足约束条件,而且具有内点算法的特性,因此收敛速度较好。最后,将该算法应用于上海证券交易所的实际数据计算,结果令人满意。作者也对所得结果进行了合理的金融实证分析。The risk-free log-optimal portfolio problem is very valuable in computational finance in practice. This paper proposes an intrinsic natural gradient-based stochastic algorithm for solving the pro-(blem). The advantage of the algorithm is that the resulting iteration vector always satisfies the constrained conditions, and it is also an interior point algorithm in essence, so has a good rate of convergence. Finally, this algorithm is applied to the real data from the Exchange Institute of Shanghai Security. The numerical results are satisfactory and the reasonable financial explanation is also suggested.

关 键 词：log-最优组合投资 黎曼流形 随机算法 最优化 无风险控制 计算金融问题 

分 类 号：F830.59[经济管理—金融学] F224.0