In this workout, we've been told that an insurance company has written some insurance business at the start of year one and ceded some of the risk to a reinsurance company. We've been asked to calculate the claims reserves and the reinsurance reserves in years one and two, assuming that all claims are settled the year after they're incurred. Now, the premiums written were 100, and the coverage period for the policies was one year.

Also, the loss ratio on those policies was 90%.

Now, in terms of the reinsurance cover, we've been told that 10 of premiums have been paid away to the reinsurance company and that these are proportionate reinsurance policies. So that means a fixed proportion of the claims can be clawed back from the reinsurer. And in this particular situation, it's going to be 10% of all future claims. But let's start off with calculating our claims reserves because we need to do that before we can calculate our reinsurance reserves. So we'll start with the beginning balance on the reserves being equal to the prior year ending balance.

Now, we need to add to this the claims incurred in year one, and we can use the loss ratio of 90% to do that, and we simply multiply that by the premiums written of 100.

Now, we need to subtract from that the claims actually paid, and we know from the question that claims are settled the year after they're incurred.

So we can just link that to the prior year claims incurred, which is clearly nil in year one. Now, let's add all that together, and that gives us the ending balance on our claims reserves for year one of 90, and we can roll forward that for year two.

And you can see that by the end of year two, that's showing as nil, and that's because all of those claims which were incurred in year one have been paid out in year two. Now, let's calculate our reinsurance reserves, and we'll start with our beginning balance being equal to our prior ending balance, and that's nil.

Now, we need to add to this the claims incurred for the reinsurer, and we know this is going to be 10% of the claims incurred by the insurance company.

So we can take our 10% from above and just multiply that by the claims incurred in our claims reserves above.

Now, we need to deduct from that the claims paid, and that's the claims paid by the reinsurance company to the insurance company.

And again, we're going to assume it's in the year after they're incurred.

So again, we'll link that to the prior year claims incurred, and that's nil in year one. Now, we can sum all that together, and that gives us an ending balance on our reinsurance reserves of nine.

Now, remember that that's an asset balance, so that nine will be shown within the assets of the insurance company.

Now, we can just roll forward all our calculations for year two, and similar to the claims reserves, you can see that those reinsurance reserves are nil by the end of year two, as the reinsurance company by then has paid back all of those claims to the insurance company.