Sparse Portfolio Selection Model Based On Group Structure

The sparse portfolio selection problem is a very important issue in the field of financial engineering,and it is also one of the hot topics in the current financial research.This paper mainly studies the sparse portfolio selection of structured assets,and proposes two kinds of sparse portfolio selection models and improves the corresponding Half threshold algorithm for numerically solving these two kinds of models,respectively.The main research contents of the thesis are as follows:Firstly,proposed theL_1/2,1 regularization theory of the unconstrained sparse structured optimization problem,and the Half threshold algorithm is constructed for solving this problem.Secondly,the group sparse portfolio selection model of structured assets is proposed.Next,based on theL_1/2,1 regularization theory and corresponding Half threshold algorithm,the Half threshold algorithm is designed to solve this model.Then,the convergence results of this algorithm is proved.The numerical experiment result shows that the proposed Half algorithm is very effective.Finally,the group sparse quantile portfolio selection model of structured assets is proposed,and the Half threshold algorithm to solve the model is constructed and its convergence is proved.Numerical experiments show that the proposed Half algorithm is more effective and feasibility.