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Tail behavior of stopped L\'evy processes with Markov modulation

Brendan Beare (), Won-Ki Seo () and Alexis Akira Toda ()

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Abstract: This article concerns the tail probabilities of a light-tailed Markov-modulated L\'evy 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.

Date: 2020-09
New Economics Papers: this item is included in nep-rmg
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