Reflected Brownian motion has been played an important role in economics, finance, queueing and many other fields. In this paper, we present the explicit spectral representation for the hitting time density of the reflected Brownian motion with two-sided barriers, and give some detailed analysis...

The extant literature on first passage problems of reflected hyper-exponential jump diffusion processes (RHEPs) lacks efficiently computable formulae for the Laplace transform of the joint distribution of the RHEP and its first passage time, cumulative distribution function of the overshoot,...

We study the cost of shocks, i.e., jump risk, with respect to reserve management when the reserve process is formulated as a drift switching jump-diffusion with a reflecting barrier at 0. Inspired by the Brownian drift switching model, our model results in a more realistic dynamic behavior of...

We propose a new numerical scheme for a class of one-dimensional reflected stochastic differential equations (SDEs) by virtue of their explicit solutions, which enables us to carry out the simulation of this class of reflected SDEs by simulating some related SDEs without reflections. The new...