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Abstract and Applied Analysis
Volume 2016, Article ID 5914657, 8 pages
http://dx.doi.org/10.1155/2016/5914657
Research Article

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

Département de Sciences de la Décision, École des HEC, Montréal, QC, Canada

Received 22 July 2016; Revised 24 August 2016; Accepted 29 September 2016

Academic Editor: Lucas Jodar

Copyright © 2016 Djilali Ait-Aoudia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.