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Chapter 6 Reinsurance programmes 6/15

Figure 6.8: EP curve
Annual probability
of exceedance
5.0%

4.0%
EP Return Loss amount
3.0% period (£m)
0.02% 5,000 40
2.0% 0.10% 1,000 30
0.20% 500 20
0.40% 250 15
1.0% 1.00% 100 5

0.0%
0 10 20 30 40 50 60 70 80

Loss amount

Reproduced with permission from Allianz Global Corporate & Specialty

The curve also yields the average annual loss (AAL) (also known as the ‘pure premium’ or the ‘burning
Curve also yields
cost’). The area under the curve represents the amount of capital necessary to cover all expected losses the AAL
over the stated time. In other words, the area under the curve is the sum of all of the average annual
losses. There is also the coefficient of variation which gives an indication of the volatility around the AAL
estimates.

Consider this… Chapter
If there is a 0.4% chance of losses exceeding US$15m in the forthcoming year, how much reinsurance cover do Reference copy for CII Face to Face Training
you buy? 6

B3 Loading

Continuing the modern actuarial approach to pricing, having established the model price by one or more
or a combination of the techniques described above, the risk is underwritten to establish a technical
price (or premium). During this step, the reinsurer may wish to load the risk premium for any number of
factors which depart from those inherent in the risk used to calculate the model premium.

As highlighted above, following a detailed analysis of the insurer’s portfolio, reinsurers may wish to load
the risk premium for the potential for extraordinary losses that could have a significant impact on the
whole account.

Example 6.9
A reinsurer reviews a property book and pays special attention to ‘high end’ risks. These might be expensive
industrial risks, such as fibre board manufacturers or large retail shopping malls. They will also consider the potential
of the portfolio to be exposed to catastrophe losses and factor that in. Extraordinary catastrophic losses may have to
be temporarily removed from the statistics to gauge the underlying basic loss history before factoring them in again
separately.

The reinsurer will consider the current terms and conditions under which the insurer is writing business
and determine the following:
• Whether there has been a change in the nature of the portfolio which could affect the basic loss
pattern. An insurer may have focused more on writing residential property instead of commercial
property which could result in a better – or worse – loss ratio.
• Underwriting changes within the company concerned.