EXPONENTIAL CONVERGENCE RATE OF RUIN PROBABILITIES FOR LEVEL-DEPENDENT LEVY-DRIVEN RISK PROCESSES

Pierre-Olivier Goffard (1) , Andrey Sarantsev (2)

1 SAF - Laboratoire de Sciences Actuarielle et Financière
2 Department of Statistics and Applied Probability

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 problem to long-term convergence of a reflected jump-diffusion to its stationary distribution, which is handled via Lyapunov functions.

Mots clés: ruin probability; uniform ergodicity; Lyapunov function; stochastically ordered process; Siegmund duality

Domaines: Probabilités [math.PR]

Pierre-Olivier Goffard, Andrey Sarantsev. EXPONENTIAL CONVERGENCE RATE OF RUIN PROBABILITIES FOR LEVEL-DEPENDENT LEVY-DRIVEN RISK PROCESSES. Journal of Applied Probability, In press. ⟨hal-01612933v3⟩