The jump diffusion process
is considered where is a standard Brownian motion, is a Poisson process with rate , and are positive constants. The i.i.d. r.v.s have a double exponential distribution given by the density
, , . The authors derive the closed-form formulae for the Laplace transform of the first passage time , , as well as for and , . Connections with renewal-type equations are discussed. The Laplace transform of the joint law of and is obtained in terms of special functions. The Gaver-Stehfest algorithm for the numerical inversion of Laplace transforms is tested.