摩擦市场中限制卖空的最优投资组合选择的算法研究

Study on Optimal Portfolio Selection for Markets with Friction and without Short Sales

证券交易过程涉及到的交易成本主要界定为印花税和佣金,该文在考虑这两种成本的基础上,构造最优投资组合选择的数学模型,并考虑限制卖空风险资产的约束条件.在模型求解过程中,首先引入极大熵函数,将目标函数中的非光滑问题光滑化;然后再引入非线性互补函数,将K-T条件下的非线性互补问题中的不等式组转化为方程组,并再次引入参数光滑化,得到一系列光滑的方程组,最后采用经典牛顿法求解.算例分析验证了该方法的有效性.

The transaction costs involved in the process of stocks trading are primarily stamp tax and commission, which constitute the basis of this paper. No short sales is taken into account. When solving the model, the maximum entropy function to smooth the objective function is introduced firstly. Then nonlinear complementarity function is introduced to transfer the inequalities into equalities, parameter is utilized to smooth them. Finally the classical Newton method is used to search for the optimal solution. Numerical test shows the validity of the method.