It is not surprising that actuaries have been daunted in their quest for an appropriate statistical model: the claim process is very complicated, particularly for ‘long tail’ business. One has to consider the incident leading to a claim, the size of the resulting claim, the time to settlement, and the distribution of payments up to the time of settlement both by amount and epoch. There are also the additional complications of inflation and investment earnings on the provisions.
In this paper, a theory is developed in which the complications of the claim process are overcome by considering the joint distribution of payments for a single claim in successive development periods. The model is distribution-free in that it does not assume specific distributions for claim size, time to settlement, or payments prior to settlement by amount and epoch. The method requires that payments which have been made be expressed in ‘constant-dollar’ terms (i.e. adjusted for past inflation).
Using this method, it is possible to obtain confidence limits for discounted future claim payments in respect of existing claims. These limits are helpful in the assessment of provisions for outstanding claims. The matrix manipulations required are easily handled by computer.
