The Annals of Applied Probability

Exit problems for spectrally negative Lévy processes and applications to (Canadized) Russian options

F. Avram, A. E. Kyprianou, and M. R. Pistorius

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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 buffer-overflow. 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 two sided exit problems are applied to solving optimal stopping problems associated with the pricing of Russian options and their Canadized versions.

Article information

Ann. Appl. Probab., Volume 14, Number 1 (2004), 215-238.

First available in Project Euclid: 3 February 2004

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Zentralblatt MATH identifier

Primary: 60J99: None of the above, but in this section
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 91B70: Stochastic models

Reflected Lévy processes exit problems scale functions American option Russian option Canadized option optimal stopping


Avram, F.; Kyprianou, A. E.; Pistorius, M. R. Exit problems for spectrally negative Lévy processes and applications to (Canadized) Russian options. Ann. Appl. Probab. 14 (2004), no. 1, 215--238. doi:10.1214/aoap/1075828052.

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