Micro-Level Stochastic Loss Reserving for General Insurance

To meet future liabilities general insurance companies will set-up reserves. Predicting future cash-flows is essential in this process. Actuarial loss reserving methods will help them to do this in a sound way. The last decennium a vast literature about stochastic loss reserving for the general insurance business has been developed. Apart from few exceptions, all of these papers are based on data aggregated in run-off triangles. However, such an aggregate data set is a summary of an underlying, much more detailed data base that is available to the insurance company. We refer to this data set at individual claim level as "micro-level data." We investigate whether the use of such micro-level claim data can improve the reserving process. A realistic micro-level data set on liability claims (material and injury) from a European insurance company is modeled. Stochastic processes are specified for the various aspects involved in the development of a claim: the time of occurrence, the delay between occurrence and the time of reporting to the company, the occurrence of payments and their size and the final settlement of the claim. These processes are calibrated to the historical individual data of the portfolio and used for the projection of future claims. Through an out-of-sample prediction exercise we show that the micro-level approach provides the actuary with detailed and valuable reserve calculations. A comparison with results from traditional actuarial reserving techniques is included. For our case-study reserve calculations based on the micro-level model are to be preferred; compared to traditional methods, they reflect real outcomes in a more realistic way