The Research On Non-life Insurance Reserving Based On Bayesian Model Averaging

The outstanding claim reserve is one of the largest debt in non-life insurance company.So it is very important for insurance companies to extract the reserve accurately.Research about claim reserving methods so far mainly include sdeterministic method and random method.The existing methods only offer the prediction of single model in reserving.However,there may be significant difference among the prediction of different models,which is called model uncertainty.If non-life insurance companies ignore the uncertainty and use a single model to predict the outstanding claim reserve,it will increase risk.The existing studies have focused on construction and estimation of reserving model and fewer studies consider the model uncertainty.Based on over-dispersed poisson model and the data that Verrall and Wuthrich(2012)used,this paper uses Bayesian model averaging to measure the model uncertainty.We use Gibbs Sampling and Metropolis Hasting algorithm to simulate the posterior samples of all models,and then we calculate posterior probability of all models through R language programming.Furthermore,the model weighted average by the posterior probability.And we use the results of the weighted average to predict the outstanding claim reserve.The results show that the Bayesian model averaging method not only get accurate outstanding claim reserve estimates,but also obtain mean square error of outstanding claim prediction which consider the model uncertainty.At the same time it avoids unnecessary loss of non-life insurance companies because of model selection.We hope that Bayesian model average method can be widely applied to non-life insurance actuarial practice and provide new insights in the claims reserving methods.