Optimal Claiming on Vehicle Insurance

Insurance companies charge reduced premiums to motorists who go through a period of one or more years without making a claim. When an accident occurs the insured frequently finds himself with the option of either making a claim and reverting to a higher premium or paying for the repair himself. Most motorists operate an informal system of "no-claim limits", whereby they only claim for repairs which exceed a certain cost.In this paper it is shown how, under reasonable assumptions regarding the rate of accidents and the distribution of repair costs, optimal no-claim limits can be determined. These minimise the long run average cost of premiums and repairs and show significant savings over the case where all claims are made. The effect of an "excess clause", whereby the insured agrees to pay a first amount of any claim is also studied, and rules for determining whether it is profitable to accept such a clause are presented in the form of a graph.