TAIL BEHAVIOR OF STOPPED LÉVY PROCESSES WITH MARKOV MODULATION

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