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#1
09-12-2018, 02:36 PM
 TDH Member CAS Non-Actuary Join Date: Dec 2016 Posts: 47

Suppose we have the following assumptions:

All reinsurance contracts renew at 1/1
Are annual

the underlying policies of the contract
are annual
on average incept at the middle of each month
have a uniform risk profile

We have claims and policy data for three underwriting (policy) years: (using the format UWY: Prem: Claim):

2016: 100: 70
2017: 80 : 70
2018: 70 : 70

I want to get the accident year figure for 2017 with these assumptions in two cases, when the reinsurance contracts are on a LOD basis and when on a RAD basis.

As all reinsurance contracts incept at 1/1 this means the premium is fully earned over two years (last underlying policy can be written at end of the year, and the policy is annual). So for a given full UW year 50% of the premium written in that year is earned and the remaining 50% is earned in the following year. I can use these percentages to get my 2017 figure

LOD:

This is where I'm stuck, if the reinsurance contracts renew at 1/1 and are on a LOD basis; how can I get the corrected earned premium? Surely the premium would be fully earned at year end which would make UWY = AY...

Last edited by TDH; 09-12-2018 at 02:42 PM..
#2
09-12-2018, 05:26 PM
 Colymbosathon ecplecticos Member Join Date: Dec 2003 Posts: 5,987

Let's add the assumption that the underlying writings are uniform.

On a risks attaching basis, you have no portfolio in. At the end of the UW year, you have a portfolio of unexpired policies that are yours. Under our assumptions, you have earned 1/2 the premium at the end of the year and will earn the other half next year, as you said. 40 in each year, assuming 2017 is the year of interest.

On a losses occurring during basis, you have a portfolio in which consists of (again, under our assumptions) of 1/2 of the previous year's underlying writings. In your example, this is a UEPR of 50. Additionally, during the year new risks will attach and you will (on average) earn help of them, so you will earn all of the previous year's 50 and half of the current year's 80, so 90 in total all earned in 2017.

It gets much more interesting if there is a premium deficiency involved.
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#3
09-13-2018, 06:17 PM
 TDH Member CAS Non-Actuary Join Date: Dec 2016 Posts: 47

Quote:
 Originally Posted by Colymbosathon ecplecticos Let's add the assumption that the underlying writings are uniform. On a risks attaching basis, you have no portfolio in. At the end of the UW year, you have a portfolio of unexpired policies that are yours. Under our assumptions, you have earned 1/2 the premium at the end of the year and will earn the other half next year, as you said. 40 in each year, assuming 2017 is the year of interest. On a losses occurring during basis, you have a portfolio in which consists of (again, under our assumptions) of 1/2 of the previous year's underlying writings. In your example, this is a UEPR of 50. Additionally, during the year new risks will attach and you will (on average) earn help of them, so you will earn all of the previous year's 50 and half of the current year's 80, so 90 in total all earned in 2017. It gets much more interesting if there is a premium deficiency involved.
Sorry could you elaborate how you got 40 in each year for the RAD basis. Let's say 2017 is the year of interest. On a RAD basis, we have the reinsurance contract renewing on 1/1 so have a maximum exposure period of 2 years. As per our assumptions we get 50% earning in the year and 50% from the previous year. Using our numbers that's 50 + 40 = 90.

This seems to coincide with your LOD basis? If a reinsurance contract incepts on 1/1 of each year, then as it's on a LOD basis it'll only cover the claims in that year, so I would think it would have a maximum exposure of a year; meaning for 2017 the 100 would be fully earned...
I am sure I'm getting it mixed up, but I don't understand the difference between the earned premium from LOD or RAD basis.
#4
09-13-2018, 09:37 PM
 Colymbosathon ecplecticos Member Join Date: Dec 2003 Posts: 5,987

Ah, here's the issue:

I assumed that your premium numbers were WP. You seem now to think that they are EP.

Look at 2017, if the premium you gave us was WP, then the underlying premium for RAD is that same amount, namely 80.

If the premium you gave us is EP, then half (in terms of exposures) of it was from UWY 2016 and the other half was from a different UWY (2017) with a different premium rate.

My answer above assumes that your figures are WP. IF they are EP, convert them to WP and modify my answer appropriately (,which, I hope, you can do.)
__________________
"What do you mean I don't have the prerequisites for this class? I've failed it twice before!"

"I think that probably clarifies things pretty good by itself."
#5
09-14-2018, 04:53 PM
 TDH Member CAS Non-Actuary Join Date: Dec 2016 Posts: 47

Quote:
 Originally Posted by Colymbosathon ecplecticos Ah, here's the issue: I assumed that your premium numbers were WP. You seem now to think that they are EP. Look at 2017, if the premium you gave us was WP, then the underlying premium for RAD is that same amount, namely 80. If the premium you gave us is EP, then half (in terms of exposures) of it was from UWY 2016 and the other half was from a different UWY (2017) with a different premium rate. My answer above assumes that your figures are WP. IF they are EP, convert them to WP and modify my answer appropriately (,which, I hope, you can do.)
Perhaps a bit more confusion but my figures are WP, I am not assuming they are EP. Right now I have a UWY 2017 figures, but i am now trying to get an Accident Year 2017 figures from this data, under both a LOD and RAD basis and I am struggling to find out how they differ on getting under an AY basis!
#6
09-14-2018, 06:27 PM
 Colymbosathon ecplecticos Member Join Date: Dec 2003 Posts: 5,987

AY 2017 losses come from 2 UWY, 2016 and 2017.

On a LOD basis, all 2017 losses count against the 2017 reinsurance.

On a RAD basis, 1/2 of the losses count against the 2016 policy and the rest against the 2017 policy.

Does that help?
__________________
"What do you mean I don't have the prerequisites for this class? I've failed it twice before!"

"I think that probably clarifies things pretty good by itself."
#7
09-14-2018, 11:39 PM
 MooBeay Member Join Date: Jan 2004 Posts: 4,776

RA: AY EP = 50+40=90
LO: AY EP = 80

Losses = 70 for both.