Premium Earning Patterns for Multi-year Policies with Aggregate Deductibles

Premium Earning Patterns for Multi-year Policies with Aggregate Deductibles

Section 1: Introduction
Statutory accounting requires that reserves be established for covered losses that have occurred but are
unpaid (loss reserves) and – effectively – for losses that have not yet occurred, but will be covered by
policies already on the books (unearned premium reserves).  Furthermore, these reserves need to be
separate.
A problem can arise when a multi-year contract has a large aggregate deductible.  If losses depleting
the deductible occur faster than expected, the premium reserve at some point in time may be
inadequate.  Of course, it is also possible that those losses occur slower than anticipated in which case
the premium reserve may be redundant.  The approach taken in this paper is that at each point in time
(or at the end of each accounting period) the pure premium portion of the unearned premium reserve
should be exactly adequate.  This, in turn, implies a certain earning pattern for the premium that, in
some cases, requires that negative premium be earned.
This paper was inspired by a discussion in my workplace on capital allocation for second-event covers
and similar types of transactions.
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  Shortly after this conversation, a very interesting discussion thread
                                                      
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 Do you need more capital to write a second-event cover than to write a first-event cover, because its results are more
volatile?  Do you need less because the probability of a loss to the cover is more remote?  (If so, once the first event occurs,
you are now effectively on a first-event cover.  Do you at this point allocate more capital?  What if you don’t have it?