LASSO-Based Simulation for High-Dimensional Multi-Period Portfolio Optimization

Abstract

This paper proposes a regression-based simulation algorithm for multi-period mean-variance portfolio (MVP) optimization problems with constraints under a high-dimensional setting. We show that the least-squares Monte Carlo (LSMC) algorithm for portfolio optimization is either unstable or degenerates in a high-dimensional portfolio. The problem stems from the estimation error of the ordinary least-squares (OLS) in the regression steps. By introducing l1-regularization technique, we greatly extend the LSMC algorithm to a high-dimensional setting. Specifically, we propose to replace the OLS by the least absolute shrinkage and selection operator (LASSO). We prove the asymptotic convergence of the novel LASSO-based simulation under such a recursive regression setting. Numerical experiments suggest our algorithm achieves great stability under both low- and higher-dimensional cases.