Comparison of stochastic reserving methods

Errata published in Australian Actuarial Journal, Vol. 13, No. 1, 2007: 719-720. In this paper, we compare and contrast several existing stochastic reserving methods under the new Australian prudential regulatory framework. These methods include Bayesian estimation with Markov chain Monte Carlo (MCMC) simulation, the chain ladder method with bootstrapping, generalised linear models (GLMs) with bootstrapping, the Kalman filter on state-space models, the Mack model, and the stochastic chain ladder method. With regard to the qualitative aspects, we investigate the methods' underlying structures, assumptions, and estimation mechanics. In particular, we devise our own structure and estimation mechanics for the stochastic chain ladder method, derive some new approximation formulae for both GLMs and the stochastic chain ladder method, and derive the covariance matrices for the Kalman filter and state-space models adopted. We find that the methods have different levels of flexibility and are suitable to different situations in practice. With regard to the quantitative aspects, we apply the methods considered to a particular claims data set. We then analyse the estimates of the expected outstanding claims liability and the risk margin for each accident year and for total. We find that the risk margin estimate of each accident year and the aggregate risk margin estimate vary considerably for different methodIncludes tables.