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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Abstract

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

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

Dates
First available in Project Euclid: 3 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1075828052

Digital Object Identifier
doi:10.1214/aoap/1075828052

Mathematical Reviews number (MathSciNet)
MR2023021

Zentralblatt MATH identifier
1042.60023

Subjects
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

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

Citation

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. https://projecteuclid.org/euclid.aoap/1075828052


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