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.

中文翻译：

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带有马尔可夫调制的停止 LÉVY 过程的尾部行为

本文涉及停在状态相关泊松率下的轻尾马尔可夫调制 Lévy 过程的尾部概率。尾部显示以特定矩阵值函数的光谱横坐标的唯一正根和负根给定的速率呈指数衰减。我们通过在一个简单的经济模型中将我们的结果应用于财富的固定分配来说明我们的结果的用途，在该模型中，具有恒定绝对风险规避的代理人会受到随机死亡率和收入波动的影响。