Hi, im really having trouble following this question. I have the answer to it but i just cant follow it. The question is: A motor insurer operates a simple no claims discount scheme with discount of 0%, 10% and 50% of the annual premium. Suppose that the insurer charges the annual premium of £2000 and that cover is provided to coincide with the calendar year. The policyholders are supposed to be divided into three groups-namely, Y, M, and O, according to their ages. The proportions of these three groups are 0.4, 0.3,and 0.3: For each policyholder the probability of having an accident during the year depends on their group identities: Group identity Probability of accident Y 0.3 M 0.1 O 0.2 The policy meets the cost of repairs which, regardless of the timing of the accident, are always carried out at the end of the year. In the event of claim free year, the policyholder moves to the next higher level of discount in the coming year. In the event of a claim during the year, the policyholder moves to the next lower level of discount, unless the policyholder belongs to the group Y. In this case, the policyholder moves in the next year to the lowest level of discount. A policyholder makes a claim following an accident if the cost of repairs is greater than the additional premiums payable at the next two renewals, assuming no further claims are made. (i) Calculate the cost of a repair below which the policyholder will not claim, for each level of discount. NOW, the answer is: Premiums: 0% level: 2000; 10% level (1 – 0.1)*2000 = 1800; 50% level (1 – 0.5)*2000 = 1000 0% discount level (category Y, M and O): cost if claim: 2000 + 1800 = 3800 cost if don’t claim: 1800 + 1000 = 2800 Difference: 3800 – 2800 = 1000 Policy holder will not claim if cost is less than £1000 10% discount level (category Y, M and O): cost if claim: 2000 + 1800 = 3800 cost if don’t claim: 1000 + 1000 = 2000 Difference: 3800 – 2000 = 1800 Policy holder will not claim if cost is less than £1800 60% discount level if in category Y cost if claim: 2000 + 1800 = 3800 cost if don’t claim: 1000 + 1000 = 2000 Difference: 3800 – 2000 = 1800 Policy holder will not claim if cost is less than £1800 60% discount level if in category M and O cost if claim: 1800 + 1000 = 2800 cost if don’t claim: 1000 + 1000 = 2000 Difference: 2800 – 2000 = 800 Policy holder will not claim if cost is less than £800 THAT's the answer, but im having trouble following it. Why is that the cost of if there is a claim, it if there isn't a claim? Any ideas? Thank you.
Tharandeep. Your question isn't very clear... if my answer doesn't resolve it then I'd recommend you amend your penultimate sentence, which currently isn't in English. The reason there is a cost when there isn't a claim is that the costs here are the costs to the policyholder not to the insurance company. So the situations being compared are "crash but don't claim" vs "crash and claim". Hope that helps Z
