Unbiased Loss Development Factors

Casualty Actuarial Society literature is inconclusive regarding whether the loss development technique is biased or unbiased, or which of the traditional methods of estimating link ratios is best. This paper presents a mathematical framework to answer those questions for the class of linear link ratio estimators used in practice. A more accurate method of calculating link ratios is derived based on classical regression theory. The circumstances under which the traditional methods could be considered optimal are discussed. It is shown that two traditional estimators may in fact be least squares estimators depending on the set of assumptions one believes governs the process of loss development. Formulas for variances of, and confidence intervals around, point estimates of ultimate loss and loss reserves are derived. A triangle of incurred loss dollars is analyzed to demonstrate the concepts and techniques. A summary of a simulation study is presented and suggests that the performance of the incurred loss development technique based on the more general least squares estimator may approach that of the Banqueter-Ferguson and Stanard-Buhlmann techniques in some situations. The requisite mathematics is within the reach of the actuarial student equipped with the first three exams. Keywords: Confidence Estimates, Econometric Modeling, Loss Development, IBNR