We use probabilistic methods to characterise the optimal exercise region of a swing option with put payoff , n%DIFDELCMD < \ge %%% 2 exercise rights and finite maturity, when the underlying asset's dynamics is specified according to the Black Scholes model . The optimal exercise region of each right (except the last) is described in terms of two boundaries which are continuous  functions of time and uniquely solve a system of coupled integral equations of Volterra-type. The swing option's price is then obtained as the sum of a European part and an early exercise premium which depends on the optimal boundaries .
We use probabilistic methods to characterise %DIFDELCMD < \ge %%% 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 . The optimal stopping region relative to each optimal stopping time is described in terms of two boundaries which are continuous , monotonic functions of time and uniquely solve a system of coupled integral equations of Volterra-type. Finally we provide a formula for the value function of the problem .
D
the optimal exercise region of a swing option with put payoff , n
D
2 exercise rights and finite maturity, when the underlying asset's dynamics is specified according to the Black
R
Scholes model
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
R
exercise region of each right (except the last)
stopping region relative to each optimal stopping time
A
, monotonic
R
The swing option's price is then obtained as the sum of a European part and an early exercise premium which depends on the optimal boundaries
Finally we provide a formula for the value function of the problem