2015 September Q7

[Jun Wu]

Dear All

Please can I check a concept with you,

In this question, we are given month delay and incurred.

What exactly does month delay mean? Is this the number of month delay after premium is written at start of each month?

I can see, solution has stated 16.25 total earned premium as at December, and this correspond to month delay 1, which has 3.5 incurred, how does this make sense?
For subsequent month delay, we adjust the incurred, and how does this formula make sense?

I have seen a few IBNR calculation question, but this is by far the most complex one.? Please let me know if there are more of this type of questions.

Much much appreciated
Best regards
Jun

 

[Busy_Bee4422]

Hi Jun

Lets begin by explaining why the incurred is being adjusted before we explain how it is being done.

The incurred claims amount shown by delay period don't have the same exposure. In our case the 3.5 m in claims incurred at delay 1 at 31 December 2014 is for all 12 months of exposure whilst the 2.5 m at delay 2 doesn't have exposure for the month of December. You therefore cannot add them together without normalising for the different exposure if you want to estimate the payment pattern. In this case the exposure is your earned premium. Its kinda like fractions where you need the same denominator before you can add them.

Delay is defined as the number of months of reporting delay in the question.

Try to visualise the information in triangle format with the amounts being incremental incurred amounts. The rows are months Jan to Dec and the columns are the delays from 1 month to 12 months. All they have done to get the 3.5 is sum the incremental amounts in the column at delay period 1, to get 2.5 they have summed at delay 2 and so forth.

Now for the column with delay 1 which will be your first column in a triangle it will have entries from January to December. The earned premium for that column will be 16.25. january earns 12 months, feb 11 months .... For the next column the earned premium is 13.8 coz the claims should have happened before December so there you remove that one month of exposure. Repeat to the last column.

To get the adjusted incurred claims for all delay periods they have adjusted to make the exposure the same earned premium in December of 16.25. Therefore at delay 2 you have 2.5 * 16.25/13.8 to get 3.0 and so forth. So when you add the amounts to get the total of 14.5 this would be the delay pattern if your exposure was 16.25 for each month.

 

[Jun Wu]

Hi Jun

Lets begin by explaining why the incurred is being adjusted before we explain how it is being done.

The incurred claims amount shown by delay period don't have the same exposure. In our case the 3.5 m in claims incurred at delay 1 at 31 December 2014 is for all 12 months of exposure whilst the 2.5 m at delay 2 doesn't have exposure for the month of December. You therefore cannot add them together without normalising for the different exposure if you want to estimate the payment pattern. In this case the exposure is your earned premium. Its kinda like fractions where you need the same denominator before you can add them.

Delay is defined as the number of months of reporting delay in the question.

Try to visualise the information in triangle format with the amounts being incremental incurred amounts. The rows are months Jan to Dec and the columns are the delays from 1 month to 12 months. All they have done to get the 3.5 is sum the incremental amounts in the column at delay period 1, to get 2.5 they have summed at delay 2 and so forth.

Now for the column with delay 1 which will be your first column in a triangle it will have entries from January to December. The earned premium for that column will be 16.25. january earns 12 months, feb 11 months .... For the next column the earned premium is 13.8 coz the claims should have happened before December so there you remove that one month of exposure. Repeat to the last column.

To get the adjusted incurred claims for all delay periods they have adjusted to make the exposure the same earned premium in December of 16.25. Therefore at delay 2 you have 2.5 * 16.25/13.8 to get 3.0 and so forth. So when you add the amounts to get the total of 14.5 this would be the delay pattern if your exposure was 16.25 for each month.

THANK YOU SO MUCH! ZIVANAIK ON ANSWERING ALL MY QUESTIONS

I get it know, i just have one more query on this please:
I see later on, we take the month delay, and match this to the EP for each month delay, ie , 2.5 for delay month 1, 2.29 for delay month 2, and so on, in order to find IBNR reserves.
I get month delay 1 correspond to 16.25 etc, but why does it also correspond to 2.5?

Also, can you teach me how to include picture in student forum please?

 

[Busy_Bee4422]

Hi Jun

Firstly the delays are being measured in months so your exposure should be measured in months. You should convert therefore your exposure to monthly units. The earned premium in December alone is 2.5m, in November alone 2.29m, Oct 2.08m alone etc ( explained in the next paragraph). The 16.25 is the earned premium for the whole year, the earned premium from January to November is 13.8m, from January to October its 11.5m etc. So there are earned premiums for individual months and then there are earned premiums for periods from January.

The 2.5 m earned premium in December, month 12, is the amount of premium earned by all the policies in force that month. Policies are written for 2.5m each month whose premium is earned evenly over the year therefore 2.5m *1/12 is the premium earned per month. So in month 12 you sold policies for all 12 months and they are each earning 2.5m * 1/12 in premium that month ie 12*2.5*1/12 =2.5m. In November, month 11, you have sold policies 11 times so the earned premium for that month is 11*2.5*1/12m = 2.29m and so forth.

To put a picture there is an icon to the right of the smiley icon that permits you to insert/attach a picture. Haven't done it myself but if you are facing issues maybe reach out to the admins.

 

[Jun Wu]

Hi Jun

Firstly the delays are being measured in months so your exposure should be measured in months. You should convert therefore your exposure to monthly units. The earned premium in December alone is 2.5m, in November alone 2.29m, Oct 2.08m alone etc ( explained in the next paragraph). The 16.25 is the earned premium for the whole year, the earned premium from January to November is 13.8m, from January to October its 11.5m etc. So there are earned premiums for individual months and then there are earned premiums for periods from January.

The 2.5 m earned premium in December, month 12, is the amount of premium earned by all the policies in force that month. Policies are written for 2.5m each month whose premium is earned evenly over the year therefore 2.5m *1/12 is the premium earned per month. So in month 12 you sold policies for all 12 months and they are each earning 2.5m * 1/12 in premium that month ie 12*2.5*1/12 =2.5m. In November, month 11, you have sold policies 11 times so the earned premium for that month is 11*2.5*1/12m = 2.29m and so forth.

To put a picture there is an icon to the right of the smiley icon that permits you to insert/attach a picture. Haven't done it myself but if you are facing issues maybe reach out to the admins.

thank you for a very quick response!
I think i get it now !!

 

[Busy_Bee4422]

Your are welcome.

 

[o.menary11]

Hi Jun

Lets begin by explaining why the incurred is being adjusted before we explain how it is being done.

The incurred claims amount shown by delay period don't have the same exposure. In our case the 3.5 m in claims incurred at delay 1 at 31 December 2014 is for all 12 months of exposure whilst the 2.5 m at delay 2 doesn't have exposure for the month of December. You therefore cannot add them together without normalising for the different exposure if you want to estimate the payment pattern. In this case the exposure is your earned premium. Its kinda like fractions where you need the same denominator before you can add them.

Delay is defined as the number of months of reporting delay in the question.

Try to visualise the information in triangle format with the amounts being incremental incurred amounts. The rows are months Jan to Dec and the columns are the delays from 1 month to 12 months. All they have done to get the 3.5 is sum the incremental amounts in the column at delay period 1, to get 2.5 they have summed at delay 2 and so forth.

Now for the column with delay 1 which will be your first column in a triangle it will have entries from January to December. The earned premium for that column will be 16.25. january earns 12 months, feb 11 months .... For the next column the earned premium is 13.8 coz the claims should have happened before December so there you remove that one month of exposure. Repeat to the last column.

To get the adjusted incurred claims for all delay periods they have adjusted to make the exposure the same earned premium in December of 16.25. Therefore at delay 2 you have 2.5 * 16.25/13.8 to get 3.0 and so forth. So when you add the amounts to get the total of 14.5 this would be the delay pattern if your exposure was 16.25 for each month.

Hi,

Could someone please explain the line "For the next column the earned premium is 13.8 coz the claims should have happened before December so there you remove that one month of exposure. Repeat to the last column." Why should the claim have happened before December?

Thanks!

 

[Darren Michaels]

Busy Bee is referring to the policies written on 1 January 2014, which will be fully earned (ie the claims have happened) by 31 December 2014.

You can find a full solution to this question in the ASET. If you need more information, it is definitely worth looking there.