Before revision: We use probabilistic methods to characterise the optimal exercise region of a swing option with put payoff , n 2 exercise rights and finite maturity, when the underlying asset's dynamics is specified according to the Black Scholes model .
After revision: We use probabilistic methods to characterise the optimal exercise region of a swing option with put payoff , n 2 exercise rights and finite maturity, when the underlying asset's dynamics is specified according to the Black time dependent optimal stopping boundaries in a problem of multiple optimal stopping on a finite time horizon. Motivated by financial applications we consider a payoff of immediate stopping of "put" type and the underlying dynamics follows a geometric Brownian motion .