Two Symmetric Families of Loss Reserving Methods

In this paper, we introduce two families of loss reserving methods – the Actual vs. Expected family and the Mean-Reverting family. The Actual vs. Expected family can be used to credibly adjust prior expectations, either in terms of a fixed initial estimate or just a prior period’s estimate, for deviations between actual and expected experience in the same direction as the deviation. In this regard, methods within this family are useful as an alternative to a fixed a priori expectation and when rolling-forward estimates of ultimate loss. Conversely, the Mean-Reverting family can be used to credibly adjust a posteriori estimates for deviations between actual and expected experience in the opposite direction of the deviation. In this regard, methods within this family are useful in situations where either the occurrence (or absence) of events decreases (or increases) the likelihood of similar events in the future.

Keywords: Reserving; Bornhuetter-Ferguson; Chain-Ladder; Benktander; Actual vs. Expected; Mean-Reversion.