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.