Loss Reserving : Past, Present and Future

The paper reviews the development of loss reserving models over the past, classifying them according to an elementary taxonomy. The taxonomic components include (1) the algebraic structure of the model, (2) the form of its parameter estimation, (3) whether or not it is explicitly stochastic, and (4) whether or not its parameters evolve over time. Particular attention is given to one of the higher species of model, involving complex structure, optimal estimation, and evolutionary parameters. A generalisation of the Kalman filter is considered as a basis of adaptive loss reserving in this case. Real life numerical examples are provided.Some implications of this type of data analysis for loss reserving are discussed, with particular reference to the form of data set used. The use of triangular arrays is questioned, and alternatives examined. Again, real life numerical examples are provided