Exponential convergence rate of ruin probabilities for level-dependent Lévy-driven risk processes

Abstract

We explicitly find the rate of exponential long-term convergence for the ruin probability in a level-dependent Lévy-driven risk model, as time goes to infinity. Siegmund duality allows to reduce the pro blem to long-term convergence of a reflected jump-diffusion to its stationary distribution, which is handled via Lyapunov functions.

arXiv comment20 pages, 5 figures