  We establish that the boundaries of the so-called Rost's reversed barrier are
the unique couple of left-continuous monotonic functions solving a suitable
system of nonlinear integral equations of Volterra type. Our result holds for
atom-less target distributions $\mu$ of the related Skorokhod embedding
problem. The integral equations we obtain here generalise the ones often
arising in optimal stopping literature and our proof of the uniqueness of the
solution goes beyond the existing results in the field.
