Reserve Ranges

[ItsaLiving]

Anyone out there know of any good articles on setting reserve ranges? I have a reserving method, but I am looking for help in determining the best way to go about setting up a range around my reserves. Articles/Papers, please?

[Arlie_Proctor]

There are several good papers on setting ranges around reserve results. See papers by the following authors (warning, these are NOT light reading):

Dr. Thomas Mack (ASTIN)
Daniel Murphy (CAS)
Son Tu (CAS)

[ItsaLiving]

Thanks for the reply! I will look into these papers. :)

[British Actuary]

The following paper was published last year and is a good summary of where stochastic reserving is at, comparing the various different methods out there in a practical context (albeit still pretty mathematical!)

If you need help getting a copy of the paper then let me know & i will sort it out for you

STOCHASTIC CLAIMS RESERVING IN GENERAL INSURANCE
England P.D.; Verrall R.J.
British Actuarial Journal, 2002, vol. 8, no. 3, pp. 443-518(76)
Faculty and Institute of Actuaries, Oxford, UK

[Klaymen]

I'd like to lay-away a stove.

[Arlie_Proctor]

British Actuary:

Is a copy of that paper available online?

[Avi]

I think this will work: STOCHASTIC CLAIMS RESERVING IN GENERAL INSURANCE (http://www.emb-d.de/SCRinGI-EnglandVerrall.pdf) but I'm not 100% sure as my home dialup is taking forever to open this.

[Brad Gile]

I think this will work: STOCHASTIC CLAIMS RESERVING IN GENERAL INSURANCE (http://www.emb-d.de/SCRinGI-EnglandVerrall.pdf) but I'm not 100% sure as my home dialup is taking forever to open this.

Good sleuthing, avi! Upon reading the abstract, this looks like it may be a gem. My download via dialup only took a few minutes, so you may just want to try again! :D

Brad

[RBLANCHARD3]

What kind of a range are you interested in? For statutory actuarial opinion purposes the "range of reasonable reserve estimates" is NOT a stochastic range. It is NOT a range of POSSIBLE reserve runoff results. Instead it IS a range of reasonable estimates of the MEAN of the reserve probability distribution.

[Wigmeister General]

A-men !!

Thus, the range of reasonable estimates should be determined by varying the underlying key assumptions of the methods used (e.g., LDFs, trend, interest rate if discounting, increased limits factors if applicable, etc.)

I'm sick and tired of seeing actuarial reports with a "range of reasonable estimates" equal to the actuary's "best estimate" plus or minus some arbitrary %.

:shake:

[reallyhopeipassed]

http://www.casact.org/pubs/forum/94spforum/94spftoc.htm

Contains links to several papers.

I am currently trying to put together a model to estimate reserve ranges. It will be fairly simple to start, and I will add to it when time permits.

Does anyone have any practical suggestions on how to start?

[Wigmeister General]

Consider how you plan to project losses. For example, if you plan to use four common methods (i.e., paid loss development, incurred loss development, paid B-F and incurred B-F), then I'd start with:

1. Low end of the range determined by LDFs that are, say, 90% better than the industry (i.e., the entity being reviewed has an experience mod of 0.90)

2. High end of the range determined by LDFs that are, say, 125% worse than the industry. Xmod of 1.25

3. For the two B-F methods, also vary expected losses based on various assumptions (e.g., if expected losses are based on loss ratio, choose the target loss ratio plus or minus some percent) and still use the "Low" and "High" LDFs.

4. Likewise, select a "Low" annual trend and a "High" annual trend.


These three sets of varying assumptions should get you started.

Later, if you plan to use other techniques (e.g. Berquist-Sherman, Fisher-Lange, Adler-Kline, etc.), you can pick key parameters to vary within these methods, too.

I'm sure, by now, you get the drift.

[reallyhopeipassed]

We have actually already completed a reserve review and come up with "best estimates" of ultimate losses. The methods used for liability lines usually were: Incurred ldf, Paid ldf, Berquist Sherman Paid & Incurred, Restated Outstanding, and Adler Kline. For property lines, we merely did the Incurred ldf & Paid ldf methods and depended mostly on the incurred method when making selections.

I now need to come up with a confidence interval of total needed reserves, for all lines of business combined. I hope to use @Risk to come up with a reasonable simulation.

To start, I came up with a table of data showing line, accident year, selected ultimate and the indicated ultimate loss under the various methods used. I then simulated each accident year/line combination with a triangle distribution where the selected ultimate was the mode, and the min and max of the various methods were the endpoints.

The problem with that method is that it assumes each accident year is independent and ended up producing a range of estimates that seemed too small. To compensate for that I summed up the accident years and did the same simulation by line. The results were more reasonable, but I am not sure whether what I did was actuarially sound.

For instance, the model assumes that whatever severity trends were used in the review are accurate, that the selected ultimates truly are the mode, and that there is a finite maximum loss.

Just curious whether you guys think I am going down the right track with this. If not, how would you approach it?

[Wigmeister General]

Trend assumption being accurate -- seems robust to me. Type II error can't be too large here.

Selected ultimate losses being the mode -- not nearly as robust. Type II error is probably larger, but not so large as to create major issues. Can you identify any inherent bias in the projections, and adjust for the bias?

Finite maximum loss -- I can't imagine there is an infinite loss possible. (Isn't there a realistic upper bound, say assets exposed?) Type II error can't be too large here.

I'd say you're in the realm of reasonableness. One alternative you could try is to apply various lognormal distributions to your results to see how large a range you get.

[reallyhopeipassed]

You are correct that we don't have an infinite upper bound for losses. (although it sometimes seems that way) I just meant that it would make sense to have a distribution that is skewed a little more to the right. Since I am just looking for a confidence interval, I don't mind an occasional extreme value.

I re-ran the model using an exponential distribution for liability lines and got a nice result. I fitted it to the various methods and ignored selection altogether.

Ready to call it a day...