A unified approach to multiple stopping and duality

The main approaches to dual representations of multiple stopping problems are the marginal and pure martingale approaches of Meinshausen and Hambly (2004) [17] and Schoenmakers (2010) [20], respectively. We show that these dual representations, as well as their more recent extensions to problems with volume constraints, can be derived in a simple unified manner using the recently developed general duality theory based on information relaxations. We also derive pure martingale representations for other multiple stopping problems, including problems with refractive index constraints.