This paper presents a framework for stochastically modeling the path of the ultimate loss ratio estimate through time from the inception of exposure to the payment of all claims. The framework is illustrated using Hayne's lognormal loss development model, but the approach can be used with other stochastic loss development models. The behavior of chain ladder and Bornhuetter-Ferguson estimates consistent with the assumptions of Hayne’s model is examined. The general framework has application to the quantification of the uncertainty in loss ratio estimates used in reserving and pricing as well as to the evaluation of risk-based capital requirements for solvency and underwriting analysis.
Michael G. Wacek (2007) studied this question.