A Bayesian Non-Linear Model for Forecasting Insurance Loss Payments

Abstract

SummaryWe propose a Bayesian non-linear hierarchical model that addresses some of the major challenges that non-life insurance companies face when forecasting the outstanding claim amounts for which they will ultimately be liable. This approach is distinctive in several ways. First, data from individual companies are treated as repeated measurements of various cohorts of claims, thus respecting the correlation between successive observations. Second, non-linear growth curves are used to model the loss development process in a way that is intuitively appealing and facilitates prediction and extrapolation beyond the range of the available data. Third, a hierarchical structure is employed to reflect the natural variation of major parameters between the claim cohorts, accounting for their heterogeneity. This approach enables us to carry out inference at the level of industry, company and/or accident year, based on the full posterior distribution of all quantities of interest. In addition, prior experience and expert opinion can be incorporated in the analyses through judgementally selected prior probability distributions. The ability of the Bayesian framework to carry out simultaneous inference based on the joint posterior is of great importance for insurance solvency monitoring and industry decision making.