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

TL;DR

This paper establishes the exponential rate at which ruin probabilities decay over time in a level-dependent Lévy-driven risk model, using duality and Lyapunov functions to analyze long-term behavior.

Contribution

It provides an explicit exponential convergence rate for ruin probabilities in complex risk models, extending understanding of their long-term stability.

Findings

Explicit exponential convergence rate derived

Reduction to reflected jump-diffusion analysis

Lyapunov functions used for stability proof

Abstract

We explicitly find the rate of exponential long-term convergence for the ruin probability in a level-dependent L\'evy-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.