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Evaluating Scale Functions of Spectrally Negative Lévy Processes

Part of: Applications Numerical methods in Fourier analysis Stochastic processes

Published online by Cambridge University Press:  14 July 2016

B. A. Surya
B. A. Surya*
Affiliation:
Bank of America
*
∗Postal address: Global Quantitative Risk Management, Quantitative Utility Department, Bank of America, N. A., 9 Raffles Place #15-00 Republic Plaza Tower 1, Singapore 048619. Email address: budhi.a.surya@bankofamerica.com
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Abstract

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In this paper we present a robust numerical method to compute the scale function W(q)(x) of a general spectrally negative Lévy process (X, P). The method is based on the Esscher transform of measure Pν under which X is taken and the scale function is determined. This change of measure makes it possible for the scale function to be bounded and, hence, makes numerical computation easy, fast, and stable. Working under the new measure Pν and using the method of Abate and Whitt (1992) and Choudhury, Lucantoni, and Whitt (1994), we give a fast stable numerical algorithm for the computation of W(q)(x).

Keywords

Lévy processspectrally negativescale functionLaplace transform

MSC classification

Secondary: 60G51: Processes with independent increments; L'evy processes 62P05: Applications to actuarial sciences and financial mathematics 65T50: Discrete and fast Fourier transforms
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 1 , March 2008 , pp. 135 - 149
Copyright
Copyright © Applied Probability Trust 2008 

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