A Note on First Passage Functionals for Lévy Processes with Jumps of Rational Laplace Transforms

This paper investigates the two-sided first exit problem for a jump process having jumps with rational Laplace transform. The corresponding boundary value problem is solved to obtain an explicit formula for the first passage functional. Also, we derive the distribution of the first passage time to t...

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Main Author:	Djilali Ait-Aoudia
Format:	Article
Language:	English
Published:	Hindawi Limited 2016-01-01
Series:	Abstract and Applied Analysis
Online Access:	http://dx.doi.org/10.1155/2016/5914657

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spelling	doaj-28a0047c2eaa44759b8d052b93e42b322020-11-24T23:21:35ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092016-01-01201610.1155/2016/59146575914657A Note on First Passage Functionals for Lévy Processes with Jumps of Rational Laplace TransformsDjilali Ait-Aoudia0Département de Sciences de la Décision, École des HEC, Montréal, QC, CanadaThis paper investigates the two-sided first exit problem for a jump process having jumps with rational Laplace transform. The corresponding boundary value problem is solved to obtain an explicit formula for the first passage functional. Also, we derive the distribution of the first passage time to two-sided barriers and the value at the first passage time.http://dx.doi.org/10.1155/2016/5914657
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Djilali Ait-Aoudia
spellingShingle	Djilali Ait-Aoudia A Note on First Passage Functionals for Lévy Processes with Jumps of Rational Laplace Transforms Abstract and Applied Analysis
author_facet	Djilali Ait-Aoudia
author_sort	Djilali Ait-Aoudia
title	A Note on First Passage Functionals for Lévy Processes with Jumps of Rational Laplace Transforms
title_short	A Note on First Passage Functionals for Lévy Processes with Jumps of Rational Laplace Transforms
title_full	A Note on First Passage Functionals for Lévy Processes with Jumps of Rational Laplace Transforms
title_fullStr	A Note on First Passage Functionals for Lévy Processes with Jumps of Rational Laplace Transforms
title_full_unstemmed	A Note on First Passage Functionals for Lévy Processes with Jumps of Rational Laplace Transforms
title_sort	note on first passage functionals for lévy processes with jumps of rational laplace transforms
publisher	Hindawi Limited
series	Abstract and Applied Analysis
issn	1085-3375 1687-0409
publishDate	2016-01-01
description	This paper investigates the two-sided first exit problem for a jump process having jumps with rational Laplace transform. The corresponding boundary value problem is solved to obtain an explicit formula for the first passage functional. Also, we derive the distribution of the first passage time to two-sided barriers and the value at the first passage time.
url	http://dx.doi.org/10.1155/2016/5914657
work_keys_str_mv	AT djilaliaitaoudia anoteonfirstpassagefunctionalsforlevyprocesseswithjumpsofrationallaplacetransforms AT djilaliaitaoudia noteonfirstpassagefunctionalsforlevyprocesseswithjumpsofrationallaplacetransforms
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A Note on First Passage Functionals for Lévy Processes with Jumps of Rational Laplace Transforms

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