A Cape Cod Model for the Exponential Dispersion Family

Abstract

Abstract The defining feature of the Cape Cod algorithm in current literature is its assumption of a constant loss ratio over accident periods. This is a highly simplifying assumption relative to the chain ladder model which, in effect, allows loss ratio to vary freely over accident period. Much of the literature on Cape Cod reserving treats it as essentially just an algorithm. It does not posit a parametric model supporting the algorithm. There are one or two exceptions to this. The present paper extends them by introducing a couple of more general stochastic models under which maximum likelihood estimation yields parameters estimates closely resembling those of the classical Cape Cod algorithm. For one of these models, these estimators are shown to be minimum variance unbiased, and so are superior to the conventional estimators, which rely on the chain ladder. A Bayesian Cape Cod model is also introduced, and a MAP estimator calculated. A numerical example is included.