C3. The Swiss Re exposure curves and the MBBEFD distribution class

Question 1

Assumptions/conditions for a valid exposure curve/limits profile

Answer 1

Assumptions:

1. scale independence: exposure curve applies regardless of IV sizes
2. all locations are at midpoint of IV ranges

different ranges of insured value are known as “limits profile”

Conditions:

1. pure prm/mid point of IV range should be constant because assume the likelihood of a given % of IV is the same for any IV size
2. should use per location profiles instead of per risk profiles because some risks may have a different # of locations which would skew results

Question 2

Considerations in different risk sizes for exposure curves (when the exposure curve assumptions are not appropriate)

Answer 2

Appropriate for homeowners insurance:
-very homogeneous, even over a large range of home size

Not appropriate for commercial insurance:

• very heterogeneous, especially construction type and occupancy
• thus exposure curves are usually constructed for different risk size groups
• for commercial LR may be very volatile so difficult to determine an expected loss ratio for the treaty period

Question 3

Considerations in consistent granularity of exposure curves

Answer 3

If some risks have multiple locations:

• make sure the IV limits profile is based on the same granularity level of the pricing
• example: if you are pricing per risk profiles, then you should use per risk IV limits profile

Question 4

Problem/solution of exposure rating

Answer 4

Problem:
-difficult to allocate gross pure premiums of each risk size group for non proportional reinsurance between the insurer and the reinsurer

Solution:

1. convert premiums to losses per risk size group using pure prm = prm * ELR
2. allocate the losses between the insurer and the reinsurer using exposure curves

Question 5

Why exposure curve using IV may exceed 100%

Answer 5

IV limits profile are generally exclude:

• homeowners: additional living expense
• commercial: business interruption

Question 6

Does the accident date underlying the curve matter at all ?

Answer 6

yes, severity distribution change over time du to inflation.
Using a curve based on different average acc date could result in using an inappropriate dristribution