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Evaluating first-passage probabilities for spectrally one-sided Lévy processes

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

L. C. G. Rogers
L. C. G. Rogers*
Affiliation:
University of Bath
*
∗ Postal address: Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK. Email address: [email protected]
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Abstract

Fast stable methods for inverting multidimensional Laplace transforms have been developed in recent years by Abate, Whitt and others. We use these methods here to compute numerically the first-passage-time distribution for a spectrally one-sided Lévy process; the basic algorithm is not easy to apply, and we have to develop a variant of it. The numerical performance is as good as the original algorithm.

Keywords

Lévy processspectrally one-sidedLaplace transformfirst-passage distribution

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory 60G51: Processes with independent increments; L'evy processes
Type
Short Communications
Information
Journal of Applied Probability , Volume 37 , Issue 4 , December 2000 , pp. 1173 - 1180
Copyright
Copyright © by the Applied Probability Trust 2000 

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