M.R.: Exit problems for spectrally negative Lévy processes and applications to (Canadized) Russian options

We consider spectrally negative Levy process and determine the joint Laplace trans form of the exit time and exit position from an interval containing the origin of the process reected in its supremum In the literature of uid models this stopping time can be identied as the time to bueroverow The Laplace transform is determined in terms of the scale functions that appear in the two sided exit problem of the given Levy process The obtained results together with existing results on two sided exit problems are applied to solving optimal stopping problems associated with the pricing of American and Russian options and their Canadized versions AMS subject classication Primary J secondary G B Key words and phrases Reected Levy processes Exit problems scale functions American option Russian option Canadized option optimal stopping In this paper we consider the class of spectrally negative Levy processes These are real valued random processes with stationary independent increments which have no positiv