02_Bernegger

Question 1

Describe what 𝑝 represents when there is NOT a maximum possible loss.

Answer 1

In this case, it’s not possible to divide 𝑋 or 𝐷 by 𝑀. Instead, we set 𝑥 = 𝑥/𝑥_0 and 𝑑 = D/𝑥_0, where 𝑋_0 is some arbitrary reference loss. Then, 𝑝 is the probability of having a loss 𝑋 that exceeds the reference loss 𝑋_0.

Question 2

An excess of loss treaty includes a reinsurance limit. Explain how to calculate the expected ceded loss using MBBEFD curves.

Answer 2

If there is no reinsurance limit, the expected ceded loss is the overall pure risk
premium times [1 − 𝐺(𝑑)].
If there is a reinsurance limit, the expected ceded loss is the overall pure risk
premium times [𝐺((Attach. point + Limit)
/MPL) − 𝐺(𝑑)].
The point is that the exposure factor decreases since there is a treaty limit.

Question 3

Explain how to fit an MBBEFD curve to price a non-proportional reinsurance treaty.

Answer 3

• Determine the 𝑔 parameter as 𝑔 = 1/p
• Calculate 𝜇 = 1/G’(0)
• Determine 𝑏 based on special cases or the general case:
  o Special Cases
  
  • If 𝜇 = 1, then 𝑏 = 0
  • If 𝜇 = (g-1)/(ln(g)*g’), then 𝑏 = 1/g
  • If 𝜇 = ln(g)/(g-1), then 𝑏 = 1
  • If 𝜇 = 1/g, then 𝑏 = ∞
    o General Case
  • Determine 𝑏 iteratively using 𝜇 = (ln(gb)(1-b))/(ln(b)(1-gb))

Question 4

Does the exposure curve represent a severity distribution or an aggregate (aka, pure premium) distribution

Answer 4

The curve represents a severity distribution. Exposure curves are used to determine the probability of losses in a layer.

Question 5

According to Bernegger, what is the main problem of exposure rating, and what are the 2 steps to solve this?

Answer 5

Bernegger says the problem in exposure rating is how to divide the total premiums of each risk size group between the ceding company and the reinsurer. Bernegger says this is solved in 2 steps:

i. Estimate the overall risk premium for each risk size group by applying an expected loss ratio to gross premiums.
ii. Divide the risk premiums into retained and ceded portions with the help of loss distribution functions.

Question 6

Does the accident date underlying the exposure curve matter at all?

Answer 6

Yes, since severity distributions change over time due to inflation. As such, using a curve based on a different average accident date could result in using an inappropriate distribution.

Question 7

Discuss whether exposure curves should be considered to be fully credible.

Answer 7

Exposure curves are usually created based on data from many risks within a company or across the industry. They are often created because individual risk experience is not credible enough to use on its own. However, this does not necessarily mean the combined data from multiple risks is fully credible, which is why curves like the MBBEFD curves can be fit to the data to try and create a smoother distribution than what appears in the original volatile loss data. Even while this may be the best alternative source of data for rating a risk, exposure curves should still be used with the consideration that they may be based on limited data or data that is less relevant to the risk being rated.

Question 8

In what situation it is appropriate to use a single exposure curve for all insured values

Answer 8

Can compare pure premium divided by midpoint, need to be consistent across all IV ranges.