Research On Sparse And Robust Portfolio Models And Their Algorithms

As one of new topics of modern finance research,the sparse robust portfolio model is a class of mathematical models obtained by applying the sparse optimization model and the robust optimization method to the portfolio selection problem.Robust optimization theory can effectively avoid the difficulties in estimating the expected return of assets such that the investment weights are more stable;and sparse optimization model can efficiently extract the optimal weights of investment options to a sparse and optimal weight vector,so as to reduce the cost of management.As a result,sparse and robust portfolio model and its algorithms have some important theoretical significance and application value.In this paper,two sparse and robust portfolio models are proposed on basis of robust portfolio models and regularization theory.And Half threshold algorithm is improved and developed into two threshold algorithms such as robust Half threshold algorithm and SP-Half threshold algorithm,which convergence results are established.The details as follows:Firstly,based on the robust portfolio model proposed by Demiguel and Nogales and the regularization theory,the sparse and robust M-portfolio model is proposed and the robust Half threshold algorithm is designed to solve the model.Then the convergence results of this algorithm are proved.The numerical experiment shows that the robust Half algorithm is much better than Lasso algorithm.Secondly,the SP-Half threshold algorithm is proposed to solve the least squares regression based on regularization theory,and its convergence results are established.The SP-Half threshold algorithm is applied to the sparse and robust portfolio model including sparse index tracking model.Numerical experiment and simulation show that SP-Half threshold algorithm is more effective.