AN OPTIMAL TRADE-OFF MODEL FOR PORTFOLIO SELECTION WITH SENSITIVITY OF PARAMETERS

被引:5
作者
Bai, Yanqin [1 ]
Wei, Yudan [1 ]
Li, Qian [1 ]
机构
[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
基金
中国国家自然科学基金;
关键词
Mean-variance model; accelerated gradient algorithm; sensitivity of parameters; quadratic programming problem; portfolio selection; CONSTRAINED QUADRATIC PROGRAMS; MARGINAL RISK CONTROL; BRANCH; ALGORITHM;
D O I
10.3934/jimo.2016055
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
In this paper, we propose an optimal trade-off model for portfolio selection with sensitivity of parameters, which are estimated from historical data. Mathematically, the model is a quadratic programming problem, whose objective function contains three terms. The first term is a measurement of risk. And the later two are the maximum and minimum sensitivity, which are non-convex and non-smooth functions and lead to the whole model to be an intractable problem. Then we transform this quadratic programming problem into an unconstrained composite problem equivalently. Furthermore, we develop a modified accelerated gradient (AG) algorithm to solve the unconstrained composite problem. The convergence and the convergence rate of our algorithm are derived. Finally, we perform both the empirical analysis and the numerical experiments. The empirical analysis indicates that the optimal trade-off model results in a stable return with lower risk under the stress test. The numerical experiments demonstrate that the modified AG algorithm outperforms the existed AG algorithm for both CPU time and the iterations, respectively.
引用
收藏
页码:947 / 965
页数:19
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