In this workout, we've been told that an insurance company has written a portfolio of insurance policies on the last day of year one.

And using the claim information below, we've been asked to calculate the claims reserve at each balance sheet date and the claims expense for each year.

Now, the written premium for the policies was 100, and the coverage period of the policies was two years. Now, we've also been given information as to how the incurred claims develop over time.

That's the first policy year and the subsequent two years.

And because that's incurred claims, that's both reported and IBNR.

And we've been given similar information as to how the payment of claims also developments during the first policy year and the subsequent two years.

Now, the first thing we're going to do is take this information from above and pop it into the table here, because we really need it laid out in a horizontal way to be able to take that and put that into a claims reserve schedule. And also, because the policy started on the last day of year one, we're effectively going to treat year two as the first policy year.

So we'll take the 35 as the first incurred claims amount and pop that here, and do the same for the 75, and then finally, the 80 we'll put in for year four.

And then exactly the same as the claims paid.

That's five for year two, 40 for year three, and 75 for year four.

Now, we can take that information and populate our claims reserve schedule. Now, as usual, we'll put the beginning amount for the claims reserve as equal to the prior year ending amount.

But we're going to add to that the claims incurred in year two.

And remember, because the information above is given on a cumulative basis, we're going to take it as the difference between year two and the prior year. Now, it doesn't make much difference in year two, but when we roll this forward, we need to always calculate it as the difference between each year.

Now, we can do exactly the same for the claims paid, but we're subtracting that amount. So we'll take the five and deduct the prior year amount.

And then when we sum all that together, that gives us the claims reserve at the end of year two of 30.

Now let's roll forward these calculations.

And you can see now how the claims reserve is building throughout years two and three as the claims are being incurred.

But then actually through years three and four, the claims are then being paid out. So by the end of year four, the claims reserve is down to five.