2016.Spring #26 a.)
I interpreted the table as there is a:
1% chance of a claim =113K,
1% + 4% = 5% chance of a claim >= 43k
1% + 4% + 5% = 10% chance of a claim >= 30k
so I used 30k in my calculation for the 10-10 rule. But I see the mark scheme used 20k.
Have they made a mistake or have I?
Comments
I think this able matched probabilities with aggregate loss outcomes. So, these are not independent events, but rather the total loss outcome in each case. So, they go straight to the 10% prob, because that is the least acceptable by the test.
yeah ok, I wondered if this were the case. I assumed they were independent since they summed to 1. Hopefully they'd accept either answer given the ambiguity. I was beginning to question whether I misunderstood percentiles
could you walk me through the sample answers?
I don't get line d.
it is -100%.
based on this, how do I know there is a 10% probability of a 10% loss to the reinsurer?
Contract #1:
a. 10% Probability of a loss corresponds to a $20,000 ground-up loss
b. Profit/Loss = $10,000 - $20,000 = -$10,000
c. Profit/Loss (as a % of premium) = -$10,000 / $10,000 = -100%
d. Contract #1 passes because there is a 10% probability of a 10% loss to the reinsurer.
b. it should be (Profit - Loss) not Profit/Loss. am I right?
c. same reason as c.
Contract #2:
based on 95%, how do I know there is not a 10% probability of a 10% loss to the reinsurer?
Thanks
1) "Profit/loss" means positive or negative income. 10K is premium, not profit.
2) The 10's in the 10-10 rule are lower bounds. Here, you have a 10% prob of a 100% loss.
3) 95% is profit, not loss. There is a 10% prob of 95% profit. At higher probabilities, the profit is even higher. So, contract does not realize a loss at the 10% prob threshold.
can I use regular method [(Loss - premium)/premium] >10%
1 (20k - 10k)/10k = 1 > 10%, yes to risk transfer
2 (500 - 10k).10k is a negative number, no to risk transfer
This works.
For this question, why are we using the gross-up losses? Shouldn't the 10% loss be based on the reinsurer's loss. Is it because only gross-up losses are given?
They are ground-up loss distributions specifically for the contracts. All of the loss represents what is ceded to the reinsurer.