Model risk and hindcast testing in claim reserving

In claims reserving, when considering variability, attention is focused on the root mean squared error of prediction, also known as the prediction error. The three components of the prediction error are: - Process risk: represents the fundamental uncertainty due to the presence of randomness when losses are generated - Parameter risk: is the uncertainty associated with the unknown parameters of statistical model - Model risk: is the risk associated with the uncertainty that the loss generating process is not represented correctly by the particular model selected. Model risk is the most difficult type of risk to measure. Traditional stochastic reserving methods, including Mack or Bootstrapping (see England and Verrall, 2002), start from a specific model (typically Chain Ladder) and ignore model risk. One way of approximating model risk is hindcast testing (see Bardis et al., 2006 and Jing et al., 2009 for case studies of U.S. insurance companies). With hindcast testing a model employs a subset of the historical data to project losses for the remainder of the historical period and compare the actual and projected results. The resulting residuals provide a proxy for model risk. This approach is non-parametric; it does not rely on the assumption of any specific underlying model. The aim of this article is to apply hindcast testing to European/Italian data, in order to estimate also the model error. References Bardis E.T., Gwilliam C. L., Lowe S.P. and Malhotra A.S (2006): Consideration Regarding Standards of Materiality in Estimates of Outstanding Liabilities http://www.casact.org/pubs/forum/06fforum/5.pdf England P. D. Verrall R. J. (2002): Stochastic Claims Reserving in General Insurance. British Actuarial Journal, 8, 443-544 Jing Yi, Lebens J. and Lowe S. (2009): Claim Reserving: Performance Testing and the Control Cycle. Variance 3:2, pp. 161-193