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

Pierre-Olivier Goffard | Zendy; Andrey Sarantsev | Zendy

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

Author(s) -

Pierre-Olivier Goffard,

Andrey Sarantsev

Publication year - 2019

Publication title -

journal of applied probability

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.668

H-Index - 59

eISSN - 1475-6072

pISSN - 0021-9002

DOI - 10.1017/jpr.2019.71

Subject(s) - mathematics , exponential function , jump , rate of convergence , exponential distribution , infinity , convergence (economics) , term (time) , lyapunov function , gamma distribution , mathematical analysis , statistics , economics , computer science , physics , channel (broadcasting) , quantum mechanics , nonlinear system , economic growth , computer network

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

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