A Least Squares Method of Producing Bornhuetter-Ferguson Initial Loss Ratios

Actuaries have relied on the Bornhuetter-Ferguson methodology in loss reserving since the "The Actuary and IBNR"[2] was published in 1972. The methodology is an intuitively appealing, credibility-weighted compromise between link ratio and expected loss ratio methods, where 'credibility' is inversely proportional to the remainder of the loss development tail. However, for almost as long as this method has been in existence, practitioners have been asking, "What do I use for my expected loss ratios?" Answers to this question (often unsatisfying ones) include industry data, company data for comparable classes of business, loss ratio pricing targets, planned loss ratios, and more. This paper addresses the above question by offering a methodology for producing underlying loss ratios for use in the Bornhuetter-Ferguson method that are derived from the data itself. In particular, this paper addresses how to determine the underlying loss ratio for the initial time period in the analysis using a least squares methodology. The initial loss ratio is then used as the seed value for all subsequent loss ratios.