The work is joint with my PhD students Yan Dolinsky and Yonathan Iron.

The talk discusses hedging for game (Israeli) style extension of swing options in discrete and continuous time considered as multiple exercise derivatives. Assuming that the underlying security can be traded without restrictions we derive formulas for valuation of multiple exercise options via classical hedging arguments. Introducing the notion of the shortfall risk for such options we produce also partial hedging which leads to minimization of this risk in the discrete time case. Previous work of Carmona and Touzi and also of other authors dealt with multiple exercise options only as multiple opti- mal stopping problems without justifying fair prices of such options by hedging arguments. Hedging of multiple exercise options required new defnitions and the extension to the game options case involves, in particular, the study of multiple stopping Dynkin's games which, especially, in the continuous time case requires substantial additional work. There are natural situations not only in energy or commodity markets where multiple exercise options can be useful, for instance, when an investor wants to buy (or sell) a stock in several installments or when a producer plans to supply overseas his product in several shipments and, say, wants to ensure a favorable exchange rate at delivery times.