  In the spirit of previous of Albrecher, Hipp, Renaud and Zhou we consider a
L\'evy insurance risk model with tax payments of a more general structure than
in the aforementioned papers that was also considered in \cite{ABBR}. In terms
of scale functions, we establish three fundamental identities of interest which
have stimulated a large volume of actuarial research in recent years. That is
to say, the two sided exit problem, the net present value of tax paid until
ruin as well as a generalized version of the Gerber-Shiu function. The method
we appeal to differs from former works in that we appeal predominantly to
excursion theory.

Probability