Simple Continuity Inequalities for Ruin Probability in the Classical Risk Model

Abstract

A simple technique for continuity estimation for ruin probability in the compound Poisson risk model is proposed. The approach is based on the contractive properties of operators involved in the integral equations for the ruin probabilities. The corresponding continuity inequalities are expressed in terms of the Kantorovich and weighted Kantorovich distances between distribution functions of claims. Both general and light-tailed distributions are considered.

Note on stability of the ruin time density in a Sparre Andersen risk model with exponential claim sizes

“…Proposition 2.1 and Theorem 2.2 below give upper bounds for d(p τ , p τ ). The relevant results on stability (continuity) of the infinite horizon ruin probability can be found, for instance, in [13,17] for the Cramer-Lundberg risk process, and for more general risk model in [2,3,9,10]. On the other hand, we are not aware of any continuity inequalities for densities of ruin time.…”

Estimaciones de estabilidad en modelos colectivos de riesgo

“…Además, el método es aplicable solamente para una clase reducida de funciones de distribución F "bien parametrizadas". En este trabajo, los resultados sobre la desigualdad (8) se presentan el Capítulo 1 y están publicados en Gordienko and Vázquez-Ortega (2016).…”