  Drawdown/regret times feature prominently in optimal stopping problems, in
statistics (CUSUM procedure) and in mathematical finance (Russian options).
Recently it was discovered that a first passage theory with general drawdown
times, which generalize classic ruin times, may be explicitly developed for
spectrally negative L\'evy processes -- see Avram, Vu, Zhou(2017), Li, Vu,
Zhou(2017). In this paper, we further examine general drawdown related
quantities for taxed time-homogeneous Markov processes, using the pathwise
connection between general drawdown and tax.
