Hello there, this is going to be a long post, any input on some/all of these questions would be highly appreciated!
Chapter 15
1. Ch 1 mentions
incurred claims = claims paid + change in reserves for outstanding claims.
- Does this mean incurred claims include IBNR, IBNER, claims handling expenses, reopened claims?
- If the above is true, can I say that incurred claims triangles already include some IBNR (hence my projection is just projecting the remaining IBNR and not the total IBNR)?
There are two definitions of incurred claims in the Glossary. The one including IBNR is used when dealing with accounts, but when dealing with triangles you use the other definition, which doesn't include IBNR. Hence this invalidates your argument.
2. Is it possible to have underwriting year as my origin year in my triangles (hence projecting the unexpired risk as well)?
Absolutely - you can use an UWYR cohort, which as you say will include an allowance for the unexpired risks in your "IBNR".
Or is it more usual to allow for unexpired risks separately?
Yes you could also allow for it separately.
You can use accident year, reporting year or underwriting year triangles and depending which one you use it affects what you are estimating.
3. In the average cost per claim method (ACPC), the example calculations seem to be using a
weighted average of
cumulative average claim amounts to obtain development factors to develop the average claim amounts to ultimate (and this is applied on the
cumulative projected ultimate claim numbers).
- However, the notes that follow mentions 'for an average claim size the volume dimension has been removed so a
simple average is more appropriate'.
- In practice question 15.5 (iii), a different approach is used - the
simple average of
incremental average claim amounts is directly applied on the
incremental projected outstanding claim numbers.
Which approach should be adopted in the exam?
Any reasonable approach would be fine as long as you explained clearly what you were doing and any assumptions you were making. The ACPC method is a family of methods rather than one single method. There was a question on this in the Sept 2021 exam where the examiners allowed several possible approaches.
Chapter 16
1. Under Section 8 - Model forms, it is mentioned that the ODP model is more flexible because individual negative increments are possible, as long as the development factor across the development period as a whole is greater than one.
- However, in Section 5, under ODP model, one of the key assumptions is that the expected incremental claims are positive for all development periods.
Can I interpret this as the following:
Individual negative increment
by claim level is acceptable, as long as the
aggregated increment over all claims in each cell of the triangle is positive (hence having development factors always >1)?
You don't need it to be positive in every cell as long as the overall increase for the column is positive the method should work.
Chapter 17
1. In section 2: Ratio of IBNR to case estimates
- Do case estimates include estimations for reopened claims, IBNER and claims handling expenses (i.e. all components of
outstanding claims except for IBNR)?
Case estimates normally only include the reported outstanding claims (and possibly CHE).
- What exactly does this ratio tell us? It is a measure of the length of the tail of the business. See Section 2.6 of Chapter 17.
2. Practice question 17.3 solutions:
- Wouldn't a deterioration of claims experience and distorting large loss increase
both the case estimates and the incurred claims (since from Ch1, incurred claims include change in reserves for outstanding claims too)? Why would these then increase the case estimates to incurred claims ratio?
They might increase both yes but if they are both not yet settled then they may lead to an increase in the case estimate to incurred ratio - it depends how material they are in relation to the existing reserves - the question is suggestion a possibility rather than saying what will always happen.
Chapter 19
1. In section 3 on non-investible funds, what does this mean: 'the insurer may decide that a smaller proportion of its other investible assets needs to be invested short'?
As the non-investible funds are not easily realisable (as they are typically held by other parties), to compensate the insurer may want to invest some of its other assets in short term assets, so they are more liquid.
Chapter 20
1. Section 2 - Steps in building and running a stochastic model
- In a stochastic model, are both my scenarios (e.g. interest rate, inflation rate) and variable outputs (e.g. claim severity) assigned probability distributions?
It is the inputs that are assigned probability distributions. The outputs therefore are stochastic variables as a result.
- What is varied to make the model 'stochastic'? e.g. if my scenario to be tested is the interest rate environment, do I take a different interest rate from its distribution on each run, while the parameters for my claim severity distribution (e.g. lognormal distribution parameters) remain the same throughout?
See above it would be your inputs that are varied whatever they may be.
- After checking the goodness of fit, we may attempt a different density function. Is this referring to the density function of the scenarios (interest rate) or variable outputs (claim severity)?
The inputs. I am not clear what your model is here, but claim severity may well be another input which can also have a probability distribution associated with it (eg lognormal).
- Similarly in sensitivity tests, we may use different distributions/parameters. Is this referring to that of the scenarios or variable outputs?
Again typically the inputs. Thee outputs are what we are trying to estimate under the scenarios being considered.
2. In section 5, under types of data, there is no mention of claims arising from unexpired risks and future business written. However, the reinsurance points do mention unexpired risks and future business.
- Are claims for unexpired risks and future business needed in the capital model? If not, why not?
Yes they would be part of the underwriting risk. This is mentioned on page 22 of Chapter 20 and further in Section 2 of Chapter 21.
Thank you for reading until the end!
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