A Synchronous Bootstrap to Account for Dependencies Between Lines of Business in the Estimation of Loss Reserve Prediction Error

In this article we consider the situation in which an insurer requires a loss reserve, together with the estimated prediction error, in respect of a number of stochastically dependent lines of business, individually and in aggregate. We suppose that generalized linear models are used to estimate each of the individual loss reserves, and that bootstrapping is used to estimate prediction errors. Specialized forms of the bootstrap, referred to as synchronous bootstraps, are constructed to capture the dependencies. Numerical examples are given in which loss reserve forecasts and their prediction errors are obtained for individual lines of business and in aggregate.