Spring 2017 26 b

Owarnock

When calculating the reinsurers paid loss, I calculated their portion of the ultimate loss as 2,550,000 * .25 = 637,500. I then subtracted the reserves of 359,375 to end with 278,125 for reinsurer paid. Looking at the solution I see this is incorrect.Can you confirm if this is a wrong approach and we should always calculate the reinsurers portion of reserves directly from the overall reserve amount and paid from the overall paid amount rather than backing into it like I explained above?

graham

In your first step where you do the calculation shown below, you are implicitly assuming the reinsurer has the same paid and reserve amounts. But the primary and reinsurer only have the same paid amounts. The reserve amounts are different.

• 25% x 2,550,000 = 637,500 <== don't do this

Here's what you should have done: First calculate the primary insurer's DIRECT paid amount:

• 2,550,000 - 1,250,000 = 1,300,000 <== primary insurer's DIRECT paid amount

The amount ceded to the reinsurer is obtained by multiplying this direct paid amount by the quota-share %:

• 25% x 1,300,000 = 325,000

Then note that:

• (primary insurer's CEDED paid) = (reinsurer's ASSUMED paid)

The reason the paid amounts are the same for the primary and reinsurer is that these paid amounts are not estimates. This is what has actually been paid to the claimant.

On the other hand, reserve amounts can be different for the primary insurer versus the reinsurer because these are estimates and each company has their own actuaries doing the estimates. The estimates should theoretically be close but they won't necessarily be the same. The primary and reinsurer may have different reserving methods and philosophies.

Owarnock

That helps a lot. Thank you!

malloryrb15

I'm a bit confused on the wording of this problem. Why is it that the reinsurer's reserves before commutation are multiplied by the 0.25? The bullet point says that the reinsurer's carried reserves are 15% higher than the insurer's carried reserves. But aren't the insurer's carried reserves just 1,250,000? Wouldn't then the reinsurer's carried reserves just be 1250000 * 1.15 instead of what the answer key says of 1250000 * 1.15 * 0.25?

Maybe I'm also misunderstanding the term "Carried Reserves" but I assumed "Carried Reserves" is essentially just the same as "Reserves".

Staff - AC

That bullet point means "reinsurer's assumed reserve is 15% higher than insurer's ceded reserve." We are talking about the reserve for the same ceded business, evaluated separately by the insurer and the reinsurer. Since insurer's direct reserve is 1,250,000, its evaluation of its ceded reserve is that times 0.25. The bullet point says the reinsurer's evaluation of what they assume is higher than this by a factor of 15%.