CAS 6 Discussion

[frummie]

Adler/Kline

I’m having trouble with the first CSM questions for Adler/Kline:

Starting in 1978, there have been three claims incurred each year (all occurring on July 1), severity trend is 10% per year, and the distribution of sizes and closing times are described below. What is the total unpaid loss liability as of December 13, 1981?

Sorry if this looks sloppy.


Closing Time Closed Claim Amt
#claims From Occurrence (1978 Acc Yr Values)
1 1 Month $100
1 1 Year $200
1 2 Years $300


The answer they give is

300*1.1^2 + 200*1.1^3 + 300x1.1^3 = 1028.50

I get that the 1 month claims will have closed by December so they are not included. I don’t get why one 300 claim (two year claims) is trended two years and one is trended three years. If a two-year claim was open 7/1/1981, it has developed for a half year and should be trended 1.5 years. For a 7/1/1980 two-year ($300) claim, by 12/31/1981 it has developed 1.5 years and only needs to be developed another half year. Similar for the one-year ($200) claim. Can anyone help?

Thanks,

frummie

[PAC]

My take:

AY 1980:
a. $300 claim trended from 7/1/80 to 7/1/82 = 300 * 1.1 ^ 2 = 363

AY 1981:
b. $200 claim trended from 7/1/79 to 7/1/82 = 200 * 1.1 ^ 3 = 266.2

c. $300 claim trended from 7/1/80 to 7/1/83 = 300 * 1.1 ^ 3 = 399.3

Total Reserve = a + b + c = 1028.5

[PAC]

I realize that I likely didn't answer your question.

You should be trending from closure date to expected closure date.

You are given, conveniently enough, that the claims remaining open at accident year age 12 months close at the middle of subsequent years; technically, at accident year ages 18 and 30 months.

You are dealing with accident year triangles, so the expected closure date is also mid-year.

These assumptions result, also conveniently enough, in the trend distances displayed in the solution.

[frummie]

Thanks!

[frummie]

OK, Here are some questions on the new McKnight article:


1. (easy) what are the superscripts in the formula for Pj on page 275, p^? (1-p)^(D-?)? I just can't see it as it is written. I'm guessing the answer is j for both.

2. Exhibit 1 page 1 column 9 (Mean Time to Default): the footnote says this comes from Exhibit 1 page 2. I don't see how. Anyone know?

Thanks,

frummie

[J.T.]

OK, Here are some questions on the new McKnight article:


1. (easy) what are the superscripts in the formula for Pj on page 275, p^? (1-p)^(D-?)? I just can't see it as it is written. I'm guessing the answer is j for both.

2. Exhibit 1 page 1 column 9 (Mean Time to Default): the footnote says this comes from Exhibit 1 page 2. I don't see how. Anyone know?

Thanks,

frummie

1. p^j (1-p)^(D-j)
2. I didn't quite understand that either. I was hoping the All10 manual (whenever they finally send it) would clarify that.

[frummie]

I don't have the new All10. Did you get the answer?

Thanks,

frummie

[J.T.]

Ok, frummie here's what I figured out finally (after sitting here for an hour, since All10 didn't give the answer).

You take the weighted average of the probablities.

Look at the Metalurgy Bond. It has 3 years of exposure left.

Using both the Incremental and Cumulative Rates respectively:
you take ((.98*1)+(1.99*2)+(2.38*3))/5.35

I got this to work for that bond and the Apple County. I'm not sure how you do a partial year like Fiberboard or Celston, but I will probably play with it when I get to that article. (I'm not on this one (review wise) yet.

Hope that helps. Let me know if you need more info.

BTW, All10 gives it this way in case it makes sense to you:

The mean time until default is the average number of years until default given that there has been a default in the policy period. This amount is calculated using incremental, as opposed to cumulative, default probabilities.