A Method for Modelling Varying Run-off Evolutions in Claims Reserving

This paper considers the application of the state space modelling to the chain ladder linear model in order to allow the run-off parameters to vary with accident year. In the usual application of the chain ladder technique, the development factors are assumed to be the same for each accident year. This implies that the run-off shape does not alter with accident year. This paper shows how this assumption can be relaxed in order to allow a recursive smooth model to be applied, or for large changes in the shape of the run-off curve. It is possible for these changes to be modelled using external inputs, or for a multiprocess model to be used to detect changes in the run-off shape. Keywords: Chain ladder technique; Kalman filter; linear models; state space models.