Convergence and asymptotic variance of bootstrapped finite-time ruin probabilities with partly shifted risk processes.

Stéphane Loisel (1) , Christian Mazza (2) , Didier Rullière (1)

1 SAF - Laboratoire de Sciences Actuarielle et Financière
2 Département de Mathématiques

The classical risk model is considered and a sensitivity analysis of finite-time ruin probabilities is carried out. We prove the weak convergence of a sequence of empirical finite-time ruin probabilities. So-called partly shifted risk processes are introduced, and used to derive an explicit expression of the asymptotic variance of the considered estimator. This provides a clear representation of the influence function associated with finite time ruin probabilities, giving a useful tool to quantify estimation risk according to new regulations.

Mots clés: Estimation Risk Solvency Margin. (ERSM); Finite-time ruin probability; robustness; Solvency II; reliable ruin probability; asymptotic normality; influence function; partly shifted risk process; Estimation Risk Solvency Margin. (ERSM).

Domaines: Economies et finances; Probabilités [math.PR]; Statistiques [math.ST]

Stéphane Loisel, Christian Mazza, Didier Rullière. Convergence and asymptotic variance of bootstrapped finite-time ruin probabilities with partly shifted risk processes.. Insurance: Mathematics and Economics, 2009, 45 (3), pp.374-381. ⟨10.1016/j.insmatheco.2009.08.003⟩. ⟨hal-00168716⟩