A Diffusion Approximation for a Markovian Queue with Reneging
Queueing Systems: Theory and Applications
Properties of the Reflected Ornstein–Uhlenbeck Process
Queueing Systems: Theory and Applications
A Jump-Diffusion Model for Option Pricing
Management Science
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
On the first passage times of reflected O-U processes with two-sided barriers
Queueing Systems: Theory and Applications
Option Pricing Under a Double Exponential Jump Diffusion Model
Management Science
Loss Rates for Lévy Processes with Two Reflecting Barriers
Mathematics of Operations Research
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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.