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

2017/10/04 by Pierre-Olivier Goffard, Andrey Sarantsev, Goffard, Pierre-Olivier +1
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #60H10 #60J60 #60J75 #91B30 #FOS: Mathematics #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Probability and Risk Models

paper · pdf · doi:10.48550/arxiv.1710.01845

openalex publication_date 2017/10/04 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

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

Related

• Fluctuations of Omega-killed level-dependent spectrally negative Lévy processes
• Explicit Rates of Exponential Convergence for Reflected Jump-Diffusions on the Half-Line
• Simultaneous Ruin Probability for Two-Dimensional Brownian and Lévy Risk Models
• Parisian excursion below a fixed level from the last record maximum of Levy insurance risk process
• Asymptotic results for exponential functionals of Levy processes