Efficient computation of first passage times in Kuo's jump-diffusion model

Abdel Belkaid, Frederic Utzet

Published 2016-04-20Version 1

S. G. Kuo and H. Wang [First Passage times of a Jump Diffusion Process \textit{Ann. Appl. Probab.} {\bf 35} (2003) 504--531] give expressions of both the (real) Laplace transform of the distribution of first passage time and the (real) Laplace transform of the joint distribution of the first passage time and the running maxima of a jump-diffusion model called Kuo model. They also propose methods to invert these transforms. In the present paper, we give a much simpler expressions of the Laplace transform of the joint distribution, we also show that these Laplace transform can be extended to the complex plane and give efficient methods to invert them. The improvement in the computing times and accuracy is remarkable.