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-00605329v1⟩