A unified approach to multiple stopping and duality

The main approaches to dual representations of multiple optimal stopping problems are the marginal and pure martingale approaches of Meinshausen and Hambly [17] and Schoenmakers [20], respectively. In this paper we show that these dual representations can be derived in a simple unified manner using the general duality theory based on information relaxations that was developed independently by Brown, Smith and Sun [7] and Rogers [19]. We also show that recent extensions of the marginal dual representation to problems with volume constraints are easily handled using this unified approach. We also derive pure martingale representations for the multiple stopping problem with volume constraints and the multiple stopping problem with so-called refractive index constraints. These last two representations are new and they can be used in practice for the pricing of swing options in electricity markets.