Using the Whole Triangle to Estimate Loss Reserves

This paper will suggest an easy, straightforward way to complement the basic methods currently used by most actuaries to estimate ultimate losses. Most actuaries use some variation of standard loss development or Bornheutter-Ferguson methods. These methods can be applied to a variety of data, e.g., paid, incurred, claim counts or average severities. The last step of most analyses is to apply a development pattern to the latest evaluation of data to estimate ultimate values. All of these methods rely, to some degree, on analyzing "data triangles" to determine the appropriate development patterns. Most actuarial papers have concentrated on the appropriate adjustments to the underlying data (e.g., Berquist-Sherman) or determining the correct way to calculate these patterns (e.g., Sherman, Weller). There is not much written on how to improve the estimate of the forecasts after the actuary has developed the factors. In this paper, I propose adding a step to the standard methods by applying the selected development pattern to all values in the data triangle. This step can be used in most methods in use by actuaries today and can be applied to data aggregated by policy year, underwriting year, accident year or report year. This paper uses accident year without loss of generality.