  In this work, we introduce a new Skorokhod problem with two reflecting
barriers when the trajectories of the driven process and the barriers are right
and left limited. We show that this problem has an explicit unique solution in
a deterministic case. Then, we apply our result to study the existence and
uniqueness of solutions of reflected stochastic differential equations with
respect to optional semimartingales. The study is carried out on a probability
space that does not necessarily satisfy the usual conditions.
