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 more general drawdown times, which generalize the classic ruin times, may be explicitly
developed for spectrally negative Levy processes. In this talk, we further examine the general drawdown related quantities in the (upward
skip-free) time-homogeneous Markov process, and then in its (general) tax process by noticing the path-wise connection between general drawdown and
tax process.