Developing individual losses for frequency-severity approach

[td290]

In chapter 14, under methods used to develop individual losses, the Course Notes state that:

For losses not in the data set, we will need to assume an ultimate size, usually based on the known losses from this cohort.

I can’t see why this is necessary. Why not just fit to the data we already have (after developing open reported claims)? The fitting of the severity distribution should not be sensitive to the number of data points we are fitting to, only to the distribution of them. It seems strange to just add data points based on the data we already have. The only thing I can see it might achieve is to cause the uncertainty in the fitted distribution parameters to be understated.

 

[Katherine Young]

Hi td290,

If we accept that we have to develop all losses, then if follows that we must also allow for IBNR claims, ie claims that have happened but which we don't yet know about.

In other words, we shouldn't let our final answer be distorted by how long it takes a policyholder to pick up the phone and tell us about a claim.

Kind regards,

Katherine.

 

[td290]

Still confused

Hi Katherine,

Thanks for this. It still doesn't make sense to me though. In fact I noticed after posting this question that the "Reinsurance pricing" chapter seems to directly contradict what you are saying. On page 22 in the ActEd study materials it states clearly:

In either approach, the development that we allow for should be incurred but not enough reported (IBNER) - ie the development of known claims, not development due to claims not yet reported.

(It then says we should develop the claim count to allow for IBNR claims when estimating the frequency distribution, but we're talking about severity here.) The advice from chapter 20 seems to make far more sense.

To pick up your point about the length of time the claimant takes to pick up the phone distorting the results, my quote from the original question does say:

usually based on known losses for this cohort.

In other words, we can assume that notification delays are independent of the severity of the claim and so the omission of the claims that have not yet been reported would not distort the severity distribution. In fact, since we know nothing about these claims yet, their omission would be less likely to distort the result than the inclusion of guesstimate figures for them.

Sorry if I'm being a bit slow to cotton on!

 

[iActuary]

I find the 4 methods to develop losses in Chapter 14 are not comparing apple to apple, in the sense that:

- Method 1 and 2 seem to find ultimate claims for reported claims
- Method 3 seems to find ultimate claims for IBNR claims
- Method 4 seems to find the distribution of ultimate claims amount (for all claims including IBNR I think?). But we are talking about developing claims here, rather than finding the distribution. So perhaps this so-called Method 4 can be incorporated in the other methods (i.e. deterministic vs stochastic)?

I think the overall idea is that we have to find the ultimate frequency and severity, in order to cover all claims (i.e. reported, IBNER and IBNR).

In practice, we are likely to use several methods (which may not even be mentioned in the notes) to derive several estimates, and select an ultimate level based on some forms of credibility.

Feedback to this topic in Chapter 14 and 20: there is certainly room for improvement. Not easy to digest!

 

[td290]

iActuary,

Your analysis of what the different methods do is of course correct. My contention is that it is not necessary to know the severities of the pure IBNR claims, only how many of them there are. Katherine’s answer doesn’t address this since it starts from an assumption that we need to know the severities of all the losses.

As I mention in my previous post, the method described in chapter 14 is not consistent with chapter 20. It is also not consistent with chapter 12 of SA3, which basically describes the integration of the frequency-severity approach with the use of extreme value theory to estimate the severity distribution:

When using extreme value theory and historical loss data to model the tail of the severity claims distribution, we should adjust the loss data for the IBNER to obtain the ultimate claims reserve for claims that have been reported.

…

When using historical loss data to model the frequency of claims exceeding the threshold, we should adjust the number of historical losses to allow for future pure IBNR losses.

But no mention of adding pure IBNR claims to the historical loss amounts. This seems sensible to me. Let’s suppose for example that we wish to fit the severity distribution by the method of moments. It is possible to obtain unbiased estimates of the mean and variance of the severity distribution from the historical loss data without the pure IBNR claims present. Making up values for the pure IBNR claims doesn't seem to me to add any credibility to the analysis. Please could somebody explain why this argument is not correct and how we can reconcile the apparent discrepancies between different sections of the Core Reading?