Source: J. Appl. Probab.
Volume 45, Number 1
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
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