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

Part of: Stochastic processes

Published online by Cambridge University Press:  22 November 2021

Florin Avram ,
Bin Li  and
Shu Li
Florin Avram*
Affiliation:
Université de Pau
Bin Li*
Affiliation:
University of Waterloo
Shu Li*
Affiliation:
Western University
*
*Postal address: Laboratoire de Mathématiques Appliquées, Université de Pau, 64013 Pau Cedex, France. Email address: florin.avram@univ-Pau.fr
**Postal address: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada. Email address: bin.li@uwaterloo.ca
***Postal address: Department of Statistical and Actuarial Sciences, Western University, London, ON, N6A 5B7, Canada. Email address: shu.li@uwo.ca
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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 more general drawdown times, which generalize classic ruin times, may be explicitly developed for spectrally negative Lévy processes [9, 20]. In this paper 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 pathwise connection between general drawdown and the tax process.

Keywords

General drawdowntax processtime-homogeneous Markov process

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 60G17: Sample path properties

Information

Type
Original Article
Information
Journal of Applied Probability , Volume 58 , Issue 4 , December 2021 , pp. 1131 - 1151
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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