Excess Losses

[Flora]

OK so I am trying to estimate the potential for losses in an excess layer. I have my ILFs and we have RAA excess loss development factors. But since nothing has ever been reported in this layer I think it is not development factors but reporting patterns/factors that we want. Because 4 years out we would probably know that a loss had hit the layer, whereas the development factors indicate that almost 40% is still unreported. SO I think we want some other measure. But the question is - what and where do I get it?

[NO1UNO]

Flora, when I've tried to estimate losses in an excess layer where none have ever been reported, I use the ILFs and exposure rate the layer. You need a premium distribution by policy limit, expected loss ratio and you need to be comfortable that the ILFs are reasonable. You haven't said that you have this additional info.

<font size=-1>[ This Message was edited by: NO1UNO on 2002-02-06 10:04 ]</font>

[Flora]

I have the ILFs from a study we do. Fairly comfortable with them.

What I am doing is looking at gross reserves for a risk retention group which is then wholly reinsured (0 net reserves). I could get premium information from the reinsurer, but we didn't really think that was something useful. Last year's actuary (different company) used a 100% loss ratio on premium to get expected losses, but that's a pretty shaky method if you ask me. I guess i am not sure what you are saying I could do with the premium info, or if it actually applies in my case.

[NO1UNO]

OK, for reserving you could do a Bornhutter-Furgson projection. You could use the 100% expected loss ratio, and reduce it to 40%, which you said is still unreported at this point. Using the 100% loss ratio is just conservative. It sounds like this layer is high enough that it will be all or nothing. Either they will never have a loss or when they do it will blow through the layer.

[Flora]

OK - we came up with expected loss using loss costs and ILFs instead of the 100% loss ratio approach used by the other actuary. Then we applied BF but I think this is high because I think that after 4 years we would know if a loss was in the layer - the LDF takes into consideration losses already reported in the layer that were underestimated, as well as those not yet know to be in the layer. My point is that none have yet been reported so I believe we are overestimating by using the full 40%.

[NO1UNO]

It could be high. It depends on what type of business the risk retention group is covering. It's very likely that their claims people have under estimated the potential of a claim. At an insurance company, I see this on a regular basis. What is you goal with this projection? Are you doing a year-end reserve review? Or are you pricing their coverage for next year?

[Flora]

reserve opinion on gross and net basis
hospital liability
they do have an open claim reserved to about 60K, but everything else is below $20K

[Arlie_Proctor]

Flora:

Depending on the source of your ILF's, you may need to adjust them to remove the risk loads before you use them to project a-priori losses in the layer. For example, the ISO ILF's contain some pretty hefty risk loads.

To obtain a lower bound for your excess relativity, you might also try fitting a heavy-tailed distribution to known losses and using the limited expected value of the fitted distribution to project excess losses. Because you have a large proportion of unreported losses, likely to be big ones, this method will likely underestimate the ultimate. This implies that the % unreported you plug into the BF for excess losses should exceed that for losses in total.

At the end of the day, you're going to have to apply a healthy dose of judgement.

Good Luck!

Arlie

[NO1UNO]

Do you know their claims reserving philosophy? Or any info about the claims? For example, at my company, the claims reserving philosophy with potentially large, but unpredictable claims is, they figure the maximum possible loss and the probablility that the claim will hit the max and set up a reserve equal to the max times the probability of the max. So, in that scenerio, the $60K claim could be a potential $6M with a 1% probability of hitting the max. Or it could really be a 60K claim.

Is there a problem if the estimate is high? Does the client want you to come up with a lower number?

[Flora]

Well, thanks for all the thoughts (I will keep checking back for more)

I think the way the analysis stands we are probably a little high, but it may stand if I don't find anything to convince the Fellow that it needs changing. He's open to change, just looking for something convincing...

[mackinac44]

If I understand the question, you've estimated the ultimate losses for a layer using a B-F method. But, you have several years of experience for the policy year with no large claims reported yet. You want to reduce the estimate of ultimate to respond to this.

I suppose that there are several methods you might use. For instance, suppose that the XS layer is $1 to $2 million. Assume the average severity is $1.5 million. If your B-F estimate of ultimate for the XS layer is $15 million, then you must be expecting 10 claims to be reported. But, after four years with no claims, you might want to consider reducing the estimate of the ultimate number of claims. To estimate the expected number of claims given information on the number of claims to date, you might consider the conditional probabilities:

P(Ult cnts = n + k | n claims at age t)

To simplify this, you might assume that k (the number of unreported claims) is independent of n (the number of reported claims):

P(k unreported claims at t | n claims at age t)

You can use a claim count development triangle to estimate the probabilities of k more claims after age t.

If you want an easy method instead, one that doesn't require any effort, then try this. Select a run-off pattern for the XS losses. The run-off pattern for XS losses should be slower than the run-off pattern for all losses. After 4 years, your current estimate for ultimate losses is the amount reported to date plus the portion of your original estimate that hasn't yet run off.

[Anonymous]

Are you

(a) putting up reserves for an experience period that is four years old,
(b) putting up reserves for a more recent experience period, or
(c) pricing for an unwritten policy?

I would contend that for (a) one wants to put up a "most likely" value, while for (c) you're looking for an "expected" value.

After four years, if you don't know of any occurrences, I'd ask "are there any statutory minimums" loss ratios for this or a similar line and post that as my "high" end of the range assuming a 100% loss ratio.

(edited for punctuation and grammer)


<font size=-1>[ This Message was edited by: MajorDeviant on 2002-02-06 12:55 ]</font>