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2014 | OriginalPaper | Buchkapitel

8. Exit Problems for Spectrally Negative Processes

verfasst von : Andreas E. Kyprianou

Erschienen in: Fluctuations of Lévy Processes with Applications

Verlag: Springer Berlin Heidelberg

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Abstract

We consider in more detail the special case of spectrally negative Lévy processes. As we have already seen in a number of examples from previous chapters, Lévy processes which have jumps in only one direction turn out to offer a significant advantage for many calculations. We devote our time in this chapter, initially, to gathering facts about spectrally negative processes from earlier chapters, and then to an ensemble of fluctuation identities which are semi-explicit in terms of a class of functions known as scale functions, whose properties we shall also explore.

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Vorheriges Kapitel Lévy Processes at First Passage

Nächstes Kapitel More on Scale Functions

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One may also argue that the terminology “scale function” is inappropriate as the mentioned analogy breaks down in a number of other respects.

This also justifies the terminology “scale function”.

See also the note at the end of this chapter.

I am grateful to Professors V.S. Korolyuk and M.S. Bratiychuk for bringing this literature to my attention.

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Titel: Exit Problems for Spectrally Negative Processes
verfasst von: Andreas E. Kyprianou
Verlag: Springer Berlin Heidelberg
Buch: Fluctuations of Lévy Processes with Applications
Print ISBN: 978-3-642-37631-3

Electronic ISBN: 978-3-642-37632-0

Copyright-Jahr: 2014
DOI: https://doi.org/10.1007/978-3-642-37632-0_8