l_1 -Regularization for multi-period portfolio selection

In this work we present a model for the solution of the multi-period portfolio selection problem. The model is based on a time consistent dynamic risk measure. We apply l_1 -regularization to stabilize the solution process and to obtain sparse solutions, which allow one to reduce holding costs. The core problem is a nonsmooth optimization one, with equality constraints. We present an iterative procedure based on a modified Bregman iteration, that adaptively sets the value of the regularization parameter in order to produce solutions with desired financial properties. We validate the approach showing results of tests performed on real data.