First passage times of reflected Ornstein-Uhlenbeck processes with two-sided jumps
In this paper we consider the first passage problem for reflected jump-type Ornstein-Uhlenbeck processes with two-reflecting barriers. We calculate the explicit joint Laplace transform of the first passage time and the corresponding undershoot when the jumps follow a two-sided mixed exponential law. The method of contour integrals proposed by Jacobsen and Jensen (in Stoch. Process. Appl. 117: 1330-1356, 2007) is applied to obtain the explicit joint Laplace transform. Finally, a comparison concerning Laplace transforms between the reflected case and non-reflected case is presented by taking smooth-pasting conditions at reflecting barriers into account.
reflected ornstein-uhlenbeck processes first passage problem two-sided mixed exponential law smooth-pasting condition