Premium Earning Patterns for Multi-year Policies with Aggregate Deductibles Part 2
appeared on CASNET. Ruy Cardoso of Ernst & Young asked a hypothetical question which I will
paraphrase here: Losses are certain at $10 per month. You cover $20 excess $100 in aggregate. The
contract begins 7/1/xx. What is the loss reserve at 12/31/xx (ignore investment income)?
After a short section defining unearned premium, the bulk of this paper consists of several examples
that illustrate some of the consequences of taking the “adequate pure premium reserve” approach to
establishing the unearned premium reserve (UEPR). The examples in this paper have been designed to
illustrate how the experience early in a multi-year contract affects the expected losses (to the contract,
not ground-up) that occur later in the contract, and how this in turn should affect premium reserving
and earning patterns. While the examples could be made more “realistic”, it was felt that this would
introduce complications not relevant to the central issue. For example, in our simplification of Ruy
Cardoso’s question above, we have assumed that there are certain losses of $20 per month. If the
losses are certain, there are questions of risk-transfer. Similarly, in Section 4, the single premium
policy has an indefinite term – even though such a policy would be highly unusual. Despite the
simplifications, the examples and the technical considerations they illustrate are relevant.
After these examples, Section 7 provides some comments on Practical Considerations, including
remarks relevant to the new requirement that an actuary opine on the adequacy of the unearned
premium reserve under certain circumstances.
The author would like to thank the reviewers and colleagues who read and commented on early
versions of this paper. The views and examples contained in this paper are those of the author. In some
cases, the approach contained herein might result, for example, in earning premium faster than somestate’s regulations would allow.