  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 differential 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.
