Anatomy of Actuarial Methods of Loss Reserving

This paper evaluates the foundation of loss reserving methods currently used by actuaries in property casualty insurance. The chain-ladder method, also known as the weighted loss development method in North America, is the most commonly used actuarial technique for loss reserving and setting liabilities for property/casualty insurers. Many actuaries believe that the basic assumption nderlying this model is the future development of losses is dependent on losses to date for each accident year. We shall see that this is not the case and the method may be rooted in the complete independence of future loss development. The alternative assumptions are, in this author’s opinion, a more natural way of analyzing the loss triangle. We shall also show that most of the methods used by actuaries are based on one common basic model, and the differences lie in how and which of the parameters are being estimated. The exposition provides some new insight to reserving methods. While it enriches our understanding of the loss reserving process and defines the common thread among various methods, it challenges some commonly held views in the actuarial profession. The exposition here points out a flaw in the Bornhuetter-Ferguson methodology as well as questions the basic framework of the loss development methodology. We shall show that we can obtain the same results as the loss development method under the assumption that the future losses are independent of what we know currently.

We introduce a new method, termed the exposure development method, which has some advantages over traditional loss development methods in some situations. The proposed methodology allows us to construct several new estimators. One can estimate the ultimate losses by combining the information gleaned from paid losses and the incurred loss triangles. Most importantly, this methodology provides better analytical tools to examine the model, look for outliers, and provides an alternative method of estimating the variability of reserves.

Keywords: Property insurance, Reserve Variability