  Motivated by Kyprianou and Zhou (2009), Wang and Hu (2012), Avram et al.
(2017), Li et al. (2017) and Wang and Zhou (2018), we consider in this paper
the problem of maximizing the expected accumulated discounted tax payments of
an insurance company, whose reserve process (before taxes are deducted) evolves
as a spectrally negative L\'{e}vy process with the usual exclusion of negative
subordinator or deterministic drift. Tax payments are collected according to
the very general loss-carry-forward tax system introduced in Kyprianou and Zhou
(2009). To achieve a balance between taxation optimization and solvency, we
consider an interesting modified objective function by considering the expected
accumulated discounted tax payments of the company until the general draw-down
time, instead of until the classical ruin time. The optimal tax return function
together with the optimal tax strategy is derived, and some numerical examples
are also provided.
