Reinsurance Pricing
The Actuarial and Underwriting Connection
by Scott Reeves
 PDF version
As actuaries become more involved in the pricing of treaty reinsurance business,
either by directly analyzing the claims experience and exposures or by an internal referral path
from underwriters, the question of whether actuaries should understand policy wordings and slips
becomes more important.
Experience pricing focuses on claims information, and
many actuaries will regularly request more years of claims
history without regard for the cover being given by the
wording of the coming period and portfolio. Claims analyses
using ever-developing techniques will be useful only
if historical claims match the terms and conditions being
offered or if some allowance is made for the differences.
Much has been written about the pricing of reinsurance
business using specific distributions and techniques. This
article presents a broader approach to pricing and some
considerations within this approach. In addition to looking
at the numbers, actuaries should consider the words
behind those numbers to provide the best results. This is
the only way to ensure the teaming of underwriters and
actuaries is aligned with business needs and goals.
What Are We Pricing?
Is it reasonable to think that slips and wordings, the traditional
responsibility of an underwriter, are aspects of the
underwriting process in which an actuary need not be involved?
After all, the actuary focuses on the numbers. But if
the contract contains a clause that is substantial in terms of
the exposures yet isn't represented in the claims experience,
then the value of the actuary's claims analysis that ignores
that clause is questionable.
How can an actuary price a piece of business without
seeing the wording or understanding the coverage being
provided? In this case, what exactly is being priced?
This is like asking a builder, "Can you build a house for
$100,000?" The likely response would be "Yes, but what do
you call a house?"
"To avoid major blunders," says Gary S. Patrik in Foundations
of Casualty Actuarial Science (2001), "an underwriter/
actuary must always understand as well as possible
the underlying primary insurance exposure and must always
be aware of the differences between the reinsurance
cover contemplated and that primary exposure."
In other words, it's important for the actuary to understand
the "reinsurance cover contemplated" and the "underlying
primary insurance exposure" within the context of the data provided to price the reinsurance
business. Not having this understanding of
both can lead to less than optimal results.
All are working together— pricing actuaries,
reserving actuaries, and
underwriters.
 It may appear obvious that the actuary
should clearly understand what's being
priced. In many cases, however, the actuary
may be involved in pricing a deal using
a simple e-mail that describes the basic
structural elements, together with a claim
file attachment.
This may certainly be
viewed as efficient, but is it
optimal?
To think differently, consider
the linked process in
Fig. 1: Take a view on the
subject, test it, and learn
from the result. Then feed
what was learned back into
the next view. This is called
the control cycle.
Then consider the interaction
between actuaries
and underwriters in reinsurance
deals—pricing and
underwriting in a collective
sense (Fig. 2):
All are working together—
pricing actuaries,
reserving actuaries, and
underwriters. Accordingly,
it makes sense for actuaries
to price the business
with a complete knowledge
of the underwriting
considerations—not at the
individual risk or exclusion level, perhaps, but certainly with a solid
understanding of what coverages are proposed
and how this relates to the historical
information received.
With this in mind, actuaries need to
explore some crucial aspects of the reinsurance
cover being provided.
Key Clauses to Consider
While there are many contract features an
actuary should understand, some of which
may be complex, there are also some simple
features that, if the actuary isn't aware,
can make pricing analysis less accurate:
The loss trigger applying to original policies;
claims made or occurrence basis?
- Should there be allowance for incurred
but not reported (IBNR) claims? Is there a
reporting tail to be considered?
- If the loss trigger is claims made, then
what is known about the exposures before
the inception of this contract? Was there a
period some years ago in which the reinsured
undertook a high-risk occupational
activity no longer undertaken but covered
under the terms of the contract?
Inception and expiry; losses occurring during
or risks-attaching?
- Under a risks-attaching definition, the
contract will be covering loss exposures for
the next 24 months, assuming all original
policies are issued for a 12-month period
and they're written evenly over the year.
- The average date for future inflation will
typically be six months later for a risks-attaching
cover than for a losses-occurring
cover.
- Under a losses-occurring treaty, unexpired
risk exposures on policies issued during
the 12 months prior to the inception of
the treaty will fall into this treaty year, so
the impact of any change in underwriting
stance for the coming year will be blended
with prior underwriting practices.
Definitions of loss/loss occurrence (including
ultimate net loss), risk, and event.
Each of these frequently used terms
can result in a very different loss analysis
according to the specific definition and
the reinsurance structure. An example is
whether losses are to be aggregated when
applying the retention on a non-proportional
treaty, or whether they're to be
treated as separate.
A painful reminder of the importance
of agreed definitions is the recent pension
mis-selling case in the United Kingdom,
Lloyds TSB General Insurance Holdings
and others v. Lloyds Bank Group Insurance
Company Limited. The decision of
the House of Lords overturned a prior
Court of Appeal decision permitting aggregation
of the losses. Each instance of
negligence was deemed by the court to be
a separate act, thereby leaving no loss to
reach the reinsurance attachment point.
The aggregate loss would have resulted in
a substantial recovery for the reinsured.
Are the insurance and reinsurance limits
expressed inclusive of costs?
Costs arising from the defense of a
claim can add a significant amount to the
indemnity payable. If the limits are exclusive
of costs, then some allowance for
costs needs to be made in the pricing of
the deal. Check to see if the data breaks
out costs separately to indemnity.
It also pays to check clauses in the
original policy. A change to original policy
deductibles is a good example.
What are the premium payment terms?
Although not a major element in the
pricing of business, the premium cash
flow should nevertheless be considered.
If the premium is to be paid 12 months
in arrears, a higher rate would certainly
be charged than for premium paid fully
at inception.
If the premium is substantial and payable
in installments over the treaty year,
one might consider the credit risk of the
cedant.
The Importance of Information
Consider the following claims experience,
presented in Table 1. There is 10
years of data on this treaty, so the information
is fairly comprehensive; certainly the usual data requirements would most
likely have been met.
But in this data period, there has been
a change in the underlying insurance
contracts. The earlier years had smaller
limits of indemnity, with several claims
at or near these limits. In the later years,
the limit has been increased—as seen
in Column B, 1999. The data should,
of course, be interpreted in light of the
proposed contract terms of the coming
reinsurance period. This requires
the actuary to understand both what is
proposed and what changes were made
during the period.
By reviewing the historical claims in
years 1991, 1994, 1996, 1997, and 1998,
shown in Column D to reflect the higher
limits offered in the coming treaty period
(perhaps by accessing claim information
on overlying, or top-up, policies), the average
loss to the layer increased substantially,
from $308,182 to $512,727, as shown
in Table 2.
In pricing such a deal using the original
loss information only, an actuary might
regard the trend toward higher claim
amounts in recent years as a feature to be
incorporated into the prediction for the
average claim size in the next year. On a
simple enough basis, this may be approximately
$700,000.
Using the adjusted losses would change
the view on this trend, as the older losses
are more in line with the recent losses. An
average claim size pick on this basis might
be $600,000, although noting the tendency
for higher claims to arise.
Of course, when the revalued claims
are seen, the predicted trend in the original
values appears excessive. But this additional
data may not have been available,
and one wouldn't be able to draw such a
comparison. The additional information
was valuable and helped the actuary avoid
taking too harsh a view on the trend when
establishing price.
Conclusion
Underwriters and actuaries should work
together, benefiting from their respective
skills and knowledge. Communication
from underwriters on changing
reinsurance terms and conditions, the
intent behind them, and underlying
exposures is invaluable to the work of
actuaries. Likewise, actuaries should
communicate their work to underwriters— the assumptions taken and the
reasons behind such assumptions. Ultimately,
underwriting and pricing can't
be considered as separate and disparate
activities.
Scott Reeves is the casualty treaty product leader, Asia Pacific P&C Reinsurance, GE Insurance Solutions, in Sydney, Australia. He can be reached at Scott.Reeves@ge.com. His is article first appeared in Casualty & Environment
Forum.
Contingencies (ISSN 1048-9851) is published by the American Academy of Actuaries, 1100 17th St. NW, 7th floor, Washington, DC 20036. The basic annual subscription rate is included in Academy dues. The nonmember rate is $24. Periodicals postage paid at Washington, DC, and at additional mailing offices. BPA circulation audited.
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