Modeling Loss Reserve Developments

The actuarial analysis of loss reserve developments begins by analyzing the patterns in historical claim data. Implicitly this analysis proceeds from a variety of assumptions, which may or may not be acknowledged or tested. By projecting loss reserves from historical data, the analyst is essentially using a mathematical model. This paper presents a general approach aimed at developing and exploring as many alternative models as possible. It is felt that there are indeed some patterns which will continue into the future; at times it may be extremely difficult to uncover these patterns or to even know that they exist. Looking backwards in time, however, it is always possible to describe what has occurred; the historical patterns may be erratic or largely meaningless, but they do exist. Likewise, at some distant future date it should be equally possible to describe the payout on the loss reserves which must now be estimated.