Hi The question asks how do we calculate the percentage change in risk premium for motor policies after the introduction of policy excess. The solution suggests calculating the total risk premium before the excess (i.e. from ground up), and the risk premium after the excess: policy excess * number of claims above the excess plus avg claim severity below excess * number of claims below excess I kept thinking I have to calculate the expected claims above the excess, then the take the ratio of this to the total risk premium from ground up, less 1 as the percentage change (because i'm looking at it from the insurer's perspective??) Where did my thought process went wrong?
Before the change you just have the total risk premium, as you suggest. But after the change, you lose the excess on all claims greater than the excess, and you lose the claim amount on all claims smaller than the excess. Not sure your method allows for this last bit?
Thanks Ian That's the part I don't understand. If i'm the insurer, i guess i would only be interested in the risk premium for all claims above the excess, as claims below the excess will be retained by the insured. So how come I need to add the last bit in the calculation of my risk premium?
Ah, I see your point now. The claims below the excess is part of the bit you're losing - ie taking it off the new risk premium. So our solution is sort of (A-B)/A whereas yours is C/A. Your method would be equivalent.
Oh! I see your point now too Your method is calculating the expected claims below the threshold. I misread the first bit as claim amounts in excess of the threshold. Thanks Ian!
