On first passage times of sticky reflecting diffusion processes with double exponential jumps

Abstract

We explore the first passage problem for sticky reflecting diffusion processes with double exponential jumps. The joint Laplace transform of the first passage time to an upper level and the corresponding overshoot is studied. In particular, explicit solutions are presented when the diffusion part is driven by a drifted Brownian motion and by an Ornstein–Uhlenbeck process.