Stochastic reserving

Mack published the prediction error of the chain ladder in the ASTIN Bulletin in 1993, without any probability distribution. England and Verrall, in 1999 and then in their 2002 review in the British Actuarial Journal, drew a full distribution from it by bootstrapping an over-dispersed Poisson model. Stochastic reserving starts there: the triangle gives a central amount, the model says how widely it can be trusted. Bayesian approaches, spread by Meyers's 2015 CAS monograph, place a prior on the parameters and simulate by MCMC, which brings expert judgment or a market loss ratio into the distribution itself. The uses are specific. Solvency II wants a one-year view, the change in the estimate over the coming twelve months (Merz and Wüthrich, 2008), narrower than the ultimate view a standard bootstrap returns. An internal model calibrates its reserve risk at the 99.5th percentile on that basis. IFRS 17 requires disclosure of the confidence level the risk adjustment corresponds to. In committee, the distribution mostly serves to say the estimate is 100 million and the range is this wide. The trap: the model sees only the triangle. Meyers showed, on the CAS database drawn from Schedule P, that Mack on incurred data produced tails that were too light and that, on paid data, both Mack and the bootstrap overstated the ultimate. Judicial inflation, a change in claims handling or a reform such as the Ogden rate cut left no cell to resample. Adding up percentiles across lines amounts to assuming perfect correlation, whereas an inflation shock hits them all in the same year. The correlation matrix selected remains a judgment call. Not to be confused with the Mack method or the ODP bootstrap taken alone, which are only two instances of it.