Author:

Keywords:

loss reserving, general insurance, poisson process, recurrent events, survival analysis, prediction

Abstract:

This paper demonstrates the merits of loss reserving using detailed information on the development of individual claims. Apart from few exceptions, the vast literature on stochastic loss reserving is developed for data aggregated in run–off triangles. However, a triangle is a summary of an underlying, more detailed, data set. We refer to this data set at individual claim level as ‘micro–level’ data. A realistic micro–level data set on liability claims from a European insurance company is analyzed. We specify a stochastic model for each event in the development of a claim: the time of occurrence of the claim, the delay between occurrence and reporting of the claim to the insurance company, the occurrence of payments and their size and the final settlement of the claim. We calibrate the resulting model to historical data and use it to project the future development of open claims. Through an out–of–sample prediction exercise we show that the micro–level approach provides the actuary with detailed and valuable reserve calculations. For the case–study developed in this paper, the micro–level model outperforms the results obtained using traditional loss reserving methods based on aggregate data.