基于双层规划的投资组合选择模型研究

Study on the portfolio selection model based on the bilevel programming

基于均值-方差投资组合选择模型,分析了市场上不存在无风险资产条件下的一类双层规划的投资组合选择问题.针对投资组合问题中参数估计不确定情形,引入了区间来描述期望收益率.通过将该问题转化为标准的极大极小问题,并借助Lagrange乘子法,得到了模型的最优投资策略和有效前沿的解析表达式.利用上海证券市场交易数据,结合数值算例分析验证了该模型在投资实践中的可行性和有效性.

Based on mean-variance model, a new portfolio selection problem for the bilevel pro- gramming was presented. The expected return was described by the interval in the portfolio se- lection problem with the estimates of parameters of uncertainty. The optimal strategy and the efficient frontier for the model which can be converted to the standard minmax problem are ob- tained by using the Lagrange multiplier method. Furthermore, a numerical example is given to show the feasibility and validity of this model in the investment practice according to the data from Shanghai Stock Exchange.