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We explicitly find the rate of exponential long-term convergence for the ruinprobability in a level-dependent L\'evy-driven risk model, as time goes toinfinity. Siegmund duality allows to reduce the pro blem to long-termconvergence of a reflected jump-diffusion to its stationary distribution, whichis handled via Lyapunov functions.

Exponential convergence rate of ruin probabilities for level-dependent L\'evy-driven risk processes