One-year reserve risk including a tail factor: closed formula and bootstrap approaches

Alexandre Boumezoued (1) , Yoboua Angoua (1) , Laurent Devineau (2, 3) , Jean-Philippe Boisseau (1)

1 R&D, Milliman, Paris
2 R&D Milliman
3 SAF - Laboratoire de Sciences Actuarielle et Financière

In this paper, we detail the main simulation methods used in practice to measure one-year reserve risk, and describe the bootstrap method providing an empirical distribution of the Claims Development Result (CDR) whose variance is identical to the closed-form expression of the prediction error proposed by Wüthrich et al. (2008). In particular, we integrate the stochastic modeling of a tail factor in the bootstrap procedure. We demonstrate the equivalence with existing analytical results and develop closed-form expressions for the error of prediction including a tail factor. A numerical example is given at the end of this study.

Mots clés: Non‐life insurance; Reserve risk; Claims Development Result; Bootstrap method; Tail factor; Prediction error; Solvency II

Domaines: Gestion des risques [q-fin.RM]

Alexandre Boumezoued, Yoboua Angoua, Laurent Devineau, Jean-Philippe Boisseau. One-year reserve risk including a tail factor: closed formula and bootstrap approaches. 2011. ⟨hal-00605329v2⟩