  We develop an explicit non-randomized solution to the Skorokhod embedding
problem in an abstract setup of signed functionals of Markovian excursions. Our
setting allows to solve the Skorokhod embedding problem, in particular, for
diffusions and their (signed, scaled) age processes, for Azema's martingale,
for spectrally one-sided Levy processes and their reflected versions, for
Bessel processes of dimension smaller than 2, and for their age processes, as
well as for the age process of excursions of Cox-Ingersoll-Ross processes. This
work is a continuation and an important generalization of Obloj and Yor (SPA
110) [35]. Our methodology, following [35], is based on excursion theory and
the solution to the Skorokhod embedding problem is described in terms of the
Ito measure of the functional. We also derive an embedding for positive
functionals and we correct a mistake in the formula in [35] for measures with
atoms.
