Reinsurance recovery?

[r_v.s]

An insurer (C) takes on a risk with EML of $10m. C has a risk excess of
loss contract $5m xs $1m with reinsurer A which applies before a surplus
treaty with reinsurer B. The surplus treaty provides a maximum
retention of $3m and 4 lines with the minimum always being ceded.
Determine how much A, B and C each pay if a claim for $9m occurs.

The solution explains- "the EML is split in the ratio 5:2:3 among A:B:C."

Given the loss is more than a million, A pays 5m.
The remaining being reinsured with B...Here is where I have a doubt...
What is the amount that is ceded under the surplus treaty?
The first layer was 5m XS 1m. Is this 1m borne entirely by C and surplus treaty applies to the remaining 4m? Or does the surplus treaty apply to the remaining 5m?

 

[Darren Michaels]

This looks like 303 Sept 2001 Q 5(iii)

The excess of loss of $5m xs $1m applies before the surplus. So the loss net of the XL applies to the surplus treaty.

Given the EML is $10m, applying the excess of loss treaty gives an EML net of the XL of $5m ($1m retention plus $4m vertical exhaustion). All of this $5m is covered by the surplus treaty.

Since the minimum is always ceded, the maximum is therefore always retained - ie $3m retained and hence $2m ceded.

Therefore EML split 5:2:3 between A:B:C.

When the claim of $9m arises, the XL applies first giving a recovery from A of $5m and the net loss remaining $4m goes to the surplus treaty where it is split between B and C in the ratio 2:3.

 

[ProCyclist]

This may sound a bit of dumb question but if the XoL is 5mln xs 1mln then surely the Surplus is applied on 6mln and above?

This is how I read it - please correct me

Layer upto 1mln = covered by insured
Layer 1mln to 6mln = 5 mln which is covered by A
Layer 6mln to 10mln = 4 mln split by B and C in proportion of 1:3

i.e 5:1:4.

So for 9mln claim
C gets the first 1mln
A gets the next 5mln (taking us to 6mln of the claim)
B gets (1/4)*(3mln) which is 0.75 mln
C gets (3/4)*(3mln) which is 2.25mln
hence the final amount split is (5,0.75,3.25) which is the alternate answer in the examiners mark scheme.

I just don't see how the excess layer finishes at 5mln if its 5mln xs 1mln

Any ideas?

 

[Katherine Young]

if the XoL is 5mln xs 1mln then surely the Surplus is applied on 6mln and above?

Not quite, the surplus applies net of XL. So EML net of XL = EML-XL recovery = 10m-5m = 5m.

Better to follow Darren's explanation above.