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Applied Mathematics and Optimization, Vol.72, No.1, 147-185, 2015
Contraction Options and Optimal Multiple-Stopping in Spectrally Negative Levy Models
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 L,vy 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.