有风险控制的log-最优投资组合问题的一个黎曼几何随机算法  

A Riemannian Geometry Underlying Stochastic Algorithm for Log-Optimal Portfolio Problem with Risk Control

作　　者：袁庆胜[1] 董承非[2] 黄建国[2] 

机构地区：[1]上海交通大学计算机科学与工程系,上海200030 [2]上海交通大学数学系,上海200240

出　　处：《上海交通大学学报》2004年第9期1552-1556,共5页Journal of Shanghai Jiaotong University

摘　　要：针对有风险控制的log-最优投资组合问题,提出了一个自适应的随机算法.该算法通过引进松弛变量,把对风险控制的不等式约束化为等式约束;再通过引进罚参数,运用罚函数法对风险控制的等式约束进行处理,从而将原来的问题化为一系列新的随机优化问题,再利用黎曼流形上的随机优化算法对其进行自适应求解.最后,使用该算法对上海证券交易所的实际数据进行了模拟计算,得到了很好的计算效果.This paper proposed an adaptively stochastic algorithm for solving a log-optimal portfolio problem with risk control. By introducing some slack variables, the original problem with inequality constraints is transformed into a new one with equality constraints, and the latter problem is further changed into a series of unconstrained stochastic optimization problems after the disposal of equality constraints (involving the risk-constraint) by virtue of the penalty function method. These new problems are then adaptively solved by some stochastic algorithms on Riemannian manifolds. Finally, the algorithm is applied to solve the risk-constrained log-optimal portfolio problem with the real data from the Institute of Shanghai Security. The numerical results are satisfactory.

关 键 词：风险控制 log-最优投资组合 自适应随机算法 黎曼流形 罚函数法 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]