  This paper studies the optimal multiple-stopping problem arising in the
context of the timing option to withdraw from a project in stages. The profits
are driven by a general spectrally negative Levy process. This allows the model
to incorporate sudden declines of the project values, generalizing greatly the
classical geometric Brownian motion model. We solve the one-stage case as well
as the extension to the multiple-stage case. The optimal stopping times are of
threshold-type and the value function admits an expression in terms of the
scale function. A series of numerical experiments are conducted to verify the
optimality and to evaluate the efficiency of the algorithm.
