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

TL;DR

This paper extends the theory of general drawdown times, crucial in optimal stopping, finance, and statistics, to taxed time-homogeneous Markov processes, building on recent developments in spectrally negative Lévy processes.

Contribution

It develops explicit results for general drawdown quantities in taxed Markov processes, linking drawdown analysis with taxation in a novel way.

Findings

Explicit formulas for drawdown-related quantities in taxed Markov processes

Connection established between drawdown times and taxation mechanisms

Extension of first passage theory to more general Markov models

Abstract

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.