Evaluating Bodily Injury Liabilities Using a Claims Closure Model

For a company which primarily writes automobile insurance the largest and most difficult liability to estimate ordinarily is the reserve for bodily injury liability coverage. It is prudent to use a variety of methods to estimate this reserve. Reserve projections depend upon a rhythm in the claims settlement process. Claims emerge at an identifiable rate, they are settled at an identifiable rate, the payments grow at an identifiable rate and the accuracy of individual case estimates improves at an identifiable rate. Standard estimation techniques rely on the last two elements, that is, on projecting cumulative payments or cumulative incurred losses using the chain ladder technique. In this paper we propose a closure model which relies on the first three elements plus the observation that serious claims are closed later than minor claims and thus the average amounts for which claims are closed increase as the claims age. The model projects the number of claims which will close and the average closure amounts at each age to derive the ultimate payments for each accident quarter. Our paper will review the major assumptions underlying the claims closure model, explain its mechanics, discuss some practical considerations, discuss its strengths and weaknesses, measure its accuracy against historical data, and discuss some possible enhancements.