On the Laplace transforms of the first exit times in one-dimensional non-affine jump-diffusion models

We compute the Laplace transforms of the first exit times for certain one-dimensional jump-diffusion processes from two-sided intervals. The method of proof is based on the solutions of the associated integro-differential boundary value problems for the corresponding value functions. We consider jump-diffusion processes solving stochastic differential equations driven by Brownian motions and several independent compound Poisson processes with multi-exponential jumps. The results are illustrated on the nonaffine pure jump analogues of certain mean-reverting or diverting diffusion processes which represent closed-form solutions of the appropriate stochastic differential equations. (C) 2016 Elsevier B.V. All rights reserved.