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 frames the development process in a least squares regression model so that those questions can be answered for link ratio estimators commonly used in practice, and for two new average development factor formulas. As a byproduct, formulas for variances of point estimates of ultimate loss and loss reserves are derived that reflect both parameter risk and process risk. An approach to measuring confidence intervals is proposed. A consolidated industry workers' compensation triangle is analyzed to demonstrate the concepts and techniques. The results of a simulation study suggest that in some situations the alternative average loss development factor (LDF) formulas may outperform the traditional estimators, and that the performance of the incurred loss development technique can approach that of the Bornhuetter-Ferguson and Stanard-Buhlmann techniques.