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

• Tác giả: Brendan K Beare, Won-Ki Seo, Alexis Akira Toda
• Ngôn ngữ: eng
• Ký hiệu phân loại: 523.887 Terminal stages
• Thông tin xuất bản: 2020
• Bộ sưu tập: Metadata
• ID: 165224

Tóm tắt

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.