• We are pleased to announce that the winner of our Feedback Prize Draw for the Winter 2024-25 session and winning £150 of gift vouchers is Zhao Liang Tay. Congratulations to Zhao Liang. If you fancy winning £150 worth of gift vouchers (from a major UK store) for the Summer 2025 exam sitting for just a few minutes of your time throughout the session, please see our website at https://www.acted.co.uk/further-info.html?pat=feedback#feedback-prize for more information on how you can make sure your name is included in the draw at the end of the session.
  • Please be advised that the SP1, SP5 and SP7 X1 deadline is the 14th July and not the 17th June as first stated. Please accept out apologies for any confusion caused.

Q&A Bank: 7.4 ii

J

jensen

Member
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?:confused:
 
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!
 
You must log in or register to reply here.
Back
Top