Exit Times, Undershoots and Overshoots for Reflected CIR Process with Two-Sided Jumps

Abstract

In this paper, we investigate the reflected CIR process with two-sided jumps to capture the jump behavior and its non-negativeness. Applying the method of (complex) contour integrals, the closed-form solution to the joint Laplace transform of the first passage time crossing a lower level and the corresponding undershoot is derived. We further extend our arguments to the exit problem from a finite interval and obtain joint Laplace transforms. Our results are expressed in terms of the real and imaginary parts of complex functions by complex matrix. Numerical results are included.