S. G. Kou and H. Wang [First passage times of a jump diffusion process, Adv. Appl. Probab. 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 Kou model. These authors invert the former Laplace transform by using Gaver-Stehfest algorithm, and for the latter they need a large computing time with an algebra computer system. In the present paper, we give a much simpler expression of the Laplace transform of the joint distribution, and we also show, using Complex Analysis techniques, that both Laplace transforms can be extended to the complex plane. Hence, we can use inversion methods based on the complex inversion formula or Bromwich integral which are very efficent. The improvement in the computing times and accuracy is remarkable.
Methodology and Computing in Applied Probability – Springer Journals
Published: Jan 7, 2017
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