General drawdown of general tax model in a time-homogeneous Markov framework

Abstract Drawdown/regret times feature prominently in optimal stopping problems, statistics (CUSUM procedure), and mathematical finance (Russian options). Recently it was discovered that a first passage theory with more general drawdown times, which generalize classic ruin may be explicitly developed for spectrally negative Lévy processes [9, 20]. In this paper we further examine the drawdown-related quantities (upward skip-free) time-homogeneous Markov process, then its (general) tax process by noticing pathwise connection between process.