L1-regularization for multi-period portfolio selection

TL;DR

This paper introduces an L1-regularized, time-consistent dynamic risk model for multi-period portfolio optimization, producing sparse solutions that reduce costs, validated through real data tests.

Contribution

It proposes a novel L1-regularization approach with a modified Bregman iteration for stable, sparse multi-period portfolio solutions based on dynamic risk measures.

Findings

Effective reduction in portfolio holding costs

Sparse solutions with desirable financial properties

Validated on real financial data

Abstract

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 l1-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.