The Application of Cumulative Distribution Functions in the Stochastic Chain Ladder Model

A new stochastic model based on the traditional chain ladder is introduced. It makes explicit use of cumulative distribution functions and payment patterns. It incorporates a mathematical rationale for non-stochastic variations in the age-to-age factors. Perturbation methods are used to obtain and justify the solution. Estimation of liabilities in the tail is a natural product of the model. All stochastic variables are assumed to be normally distributed, and the assumption is then confirmed with the chi square goodness-of-fit test. Extensive numerical solutions of an actual problem are given. Several new avenues of related research are suggested.