Resumen
We investigate some important probabilistic properties relating to the first passage time of a hyper-exponential jump diffusion process, including its finiteness, expectation, conditional memorylessness, and conditional independence. Moreover, the joint distribution of the first passage time and the overshoot is studied from a primal–dual perspective.

Resumen
In this paper we present a Laplace transform-based analytical solution for pricing double-barrier options under a flexible hyper-exponential jump diffusion model (HEM). The major theoretical contribution is that we prove non-singularity of a related high-dimensional matrix, which guarantees the existence and uniqueness of the solution.