Weak Limits of Random Coefficient Autoregressive Processes and their Application in Ruin Theory

Yuchao Dong , Jérôme Spielmann (1, 2)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques
2 UA - Université d'Angers

We prove that a large class of discrete-time insurance surplus processes converge weakly to a generalized Ornstein-Uhlenbeck process, under a suitable re-normalization and when the time-step goes to 0. Motivated by ruin theory, we use this result to obtain approximations for the moments, the ultimate ruin probability and the discounted penalty function of the discrete-time process.

Mots clés: Invariance principle; Weak convergence; Autoregressive processes; Stochastic recurrence equations; Generalized Ornstein-Uhlenbeck process; Ruin probability; First passage time

Domaines: Probabilités [math.PR]; Gestion des risques [q-fin.RM]

Yuchao Dong, Jérôme Spielmann. Weak Limits of Random Coefficient Autoregressive Processes and their Application in Ruin Theory. 2019. ⟨hal-02170829v1⟩