FALL 2014, Q17

actuaryp24

In the solution provided, why are there 2 separate payment patterns for AY 2012 and AY 2013?

Staff-T1

This is because at Dec 31 2013, AY 2012 ( 2 years remaining to complete payout) is at a different maturity level than AY 2013 (3 years remaining to complete payout)

actuaryp24

I am very confused. Why would that need to be taken into consideration?

Staff-T1

Right now we are at Dec 31, 2013:

• AY 2012 is currently 24 months old with 30% of payments remaining (1 - Cumulative paid @ 24 months)
• AY 2013 is currently 12 months old with 50% of payments remaining (1 - Cumulative paid @ 12 months)

Taking just the next 12 months payment pattern as an example ~
For AY 2012, the payment pattern would be different vs AY 2013 because in the next 12 months, 15% of the ultimate claims will be paid out while there is currently 30% of the ultimate claims pending. This means that 50% (15%/30%) of the current unpaid will be paid in the next period.
For AY 2013, 20% of the ultimate claims will be paid out while there is currently 50% of the ultimate claims pending. This means that 40% (20%/50%) of the current unpaid will be paid in the next period.

zezima

The examiner's report says that the Net Unpaid for AY 2012 is 47,500 but shouldn't it be 35,625?

Here's how I arrive at my answer:

AY 2012:
Gross Ult Losses - Gross Cumulative Paid Losses = Gross Unpaid Losses
157500-110000 = 47,500

Since there's a 25% quota share treaty (ie insurer cedes 25% and retains 75%),

Net Unpaid Losses = 45,500 * 0.75 = 35,625

Is the examiner's report wrong or have I missed something? This is the only thing causing my final answer to be different than what the examiner's report shows.

Staff-T1

The reinsurance agreement is only effective for AY 2013 and later. You wouldn't apply the QS on AY 2012 as you have above

zezima

Thanks