Consistent development patterns

Abstract

Traditional claim estimation in general insurance works with accident year cohorts and development patterns. For the impending International Financial Reporting Standard (IFRS) 17 Insurance Contracts and often for reinsurance purposes, claim estimates must be split by contract year. This paper proposes to add contract year as a cohort classifier and to adjust the development patterns accordingly. To this end, we use the continuous time models of Hesselager and Norberg. Having contract year as an additional cohort classifier, display of claim estimates by contract year and/or accident year becomes a simple matter of summation across the appropriate dimensions. The continuous time model also enables us to derive mutually consistent development patterns for discrete time intervals of different length, such as years and quarters. In addition to delivering consistent development patterns in discrete time, continuous time modelling offers the advantage of requiring only a fixed number of model parameters. Although most of the derivations in this paper are explained in terms of claim numbers, the mechanics can also be applied to claim payments.