Relationship between least squares Monte Carlo and approximate linear programming

Least squares Monte Carlo (LSM) is commonly used to manage and value early or multiple exercise financial or real options. Recent research in this area has started applying approximate linear programming (ALP) and its relaxations, which aim at addressing a possible ALP drawback. We show that regress-later LSM is itself an ALP relaxation that potentially corrects this ALP shortcoming. Our analysis consolidates two streams of research and supports using this LSM version rather than ALP on the considered models.