Reserving consecutive layers of inwards excess-of-loss reinsurance

Consider an excess-of-loss reinsurance arranged in a number of layers. A loss reserve is required for each layer. There are two major reasons why the independent application of some conventional loss reserving technique to each layer is inappropriate. First, the experiences in different layers in respect of a particular treaty year will be linked; favourable or adverse experience in one layer is likely to be reflected in favourable or adverse experience in the next. Second, experience data will typically become sparse in the higher layers, rendering analysis in isolation from other layers relatively uninformative. The purpose of the present paper is to analyse the linkages between the loss experiences of different layers, and apply these to obtain linked loss reserves. A numerical example is provided.