This must the toughest nut to crack. In the second line of solution (i), I thought 14 risk units is for the entire year, so multiplying it by 12 in the next line did not make sense to me. Could anyone please explain more? Also in part (i) of the solution, I get the unit exposures for Jan - April; April = 4 coz it's 1.5 (Feb) + 1.5 (Mar) + 1.0 (Apr) since Jan claims are settled already by March. How do I reason May - Dec? I expected 3.5 for May, 3.0 for Jun-Nov, and 3.5 for Dec. On the following page, how did we arrive at 48 units paid, 21 O/S, and 18 units IBNR? I stopped there and got lost in the rest. Help!
Don't worry Jensen, a lot of people struggle with this question. The good news is that once you've grasped the technique, all future questions look much easier! Your logic for exposure in each month is not quite right. Once you've sorted that out the rest of the answer should follow with less difficulty. You need to remember that: the premium earned in January relates to business written in January (1.5 units) the premium earned in February relates to business written in January and February (2 x 1.5=3) the premium earned in March relates to business written in Jan, Feb and March (3 x 1.5=4.5) the premium earned in April relates to business written in Jan, Feb, Mar and April (4 x 1 = 4) ... and so on. I've attached a spreadsheet that gives the calculation for each month. The row at the bottom gives the total units earned in each calendar month, and I've also shown the amounts of paid, O/S and IBNR claims as at the end of December. Have a look at it and see how you get on. Kind regards, Katherine.
