Exit problems for spectrally negative L�vy processes and applications to (Canadized) Russian options

M. R. Pistorius, A. E. Kyprianou, F. Avram
2004 The Annals of Applied Probability  
We consider spectrally negative Lévy process and determine the joint Laplace transform of the exit time and exit position from an interval containing the origin of the process reflected in its supremum. In the literature of fluid models, this stopping time can be identified as the time to bufferoverflow. The Laplace transform is determined in terms of the scale functions that appear in the two-sided exit problem of the given Lévy process. The obtained results together with existing results on
more » ... isting results on two sided exit problems are applied to solving optimal stopping problems associated with the pricing of Russian options and their Canadized versions.
doi:10.1214/aoap/1075828052 fatcat:rhghsdaqbva25a3zyetrphtcau