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TAIL BEHAVIOR OF STOPPED LÉVY PROCESSES WITH MARKOV MODULATION

Published online by Cambridge University Press:  13 July 2021

Brendan K. Beare*
Affiliation:
University of Sydney
Won-Ki Seo
Affiliation:
University of Sydney
Alexis Akira Toda
Affiliation:
University of California San Diego
*
Address correspondence to Bredan K. Beare, School of Economics, University of Sydney, Sydney, Australia; e-mail: brendan.beare@sydney.edu.au.

Abstract

This article concerns the tail probabilities of a light-tailed Markov-modulated Lévy process stopped at a state-dependent Poisson rate. The tails are shown to decay exponentially at rates given by the unique positive and negative roots of the spectral abscissa of a certain matrix-valued function. We illustrate the use of our results with an application to the stationary distribution of wealth in a simple economic model in which agents with constant absolute risk aversion are subject to random mortality and income fluctuation.

Type
ARTICLES
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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