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            <title xml:lang="en">Continuous-time modeling and bootstrap for chain ladder reserving</title>
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              <p>We revisit the famous Mack's model which gives an estimate for the mean square error of prediction of the chain ladder claims reserves. We introduce a stochastic dierential equation driven by a Brownian motion to model accumulated total claims amount for the chain ladder method. Within this continuous-time framework, we propose a bootstrap technique for estimating the distribution of claims reserves. It turns out that our approach leads to inherently capturing asymmetry and non-negativity, eliminating the necessity for additional assumptions. We conclude with a case study and comparative analysis against alternative methodologies based on Mack's model.</p>
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              <p>Nous revisitons le célèbre modèle de Mack qui fournit une estimation de l'erreur quadratique moyenne de la prédiction des provisions de sinistres selon la méthode de chain ladder. Nous introduisons une équation différentielle stochastique pilotée par un mouvement brownien pour modéliser le montant total cumulé des sinistres dans la méthode de chain ladder. Dans ce cadre à temps continu, nous proposons une technique de bootstrap pour estimer la distribution des provisions de sinistres. Il s'avère que notre approche permet de capturer intrinsèquement l'asymétrie et la positivité, éliminant ainsi le besoin d'hypothèses supplémentaires. Nous concluons par une étude de cas et une analyse comparative par rapport à des méthodologies alternatives construites sur le modèle de Mack.</p>
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