With certain adjustments, traditional estimators may also be used for the statutory Unearned Premium Reserve, or UPR, for long-duration contracts. This reserve is governed by SSAP 65, the most important requirement of which is “Test 2”, that earnings be recognized in proportion to the expected emergence of losses and expenses. Here the estimators model unincurred losses by issue month versus lag to incurral. The result of greatest interest is now the set of lag, or earnings, factors.
Adjustments are necessary to accommodate the decline in exposure due to cancellations, the deficiency of recent diagonals in the issue-to -incurral lag triangle due to unreported losses, and the unusual shapes and weight of tails for immature business. In particular, it is convenient to develop not losses per se but partial loss ratios to premium remaining in force, thus “factoring out” the effect of cancellations and leaving the results correct on a no-cancellation basis.
In this paper we suggest taking this adjustment one step further, and developing loss ratios to the product of premium in force and a set of positive a-priori earnings factors, the final earnings factors being the product of the a-priori factors and these “residual” earnings factors. In the case of automobile extended service contracts, there exists an excellent model for such a-priori factors, published by Kerper and Bowron in 2007 [1], but the technique is not dependent on any particular underlying model.
We demonstrate that this procedure (a) improves the robustness of the estimators to lack of perfect homogeneity in the data, (b) greatly simplifies the specification and calculation of tail factors, and (c) facilitates the use of reference factors to improve the estimates at lags where the experience data is sparse.
Keywords: Unearned Premium Reserve, Reserving,
