Modeling accounting year dependence in runoff triangles

Abstract

Typically, non-life insurance claims data is studied in claims development triangles which display the two time axes accident years and development years. Most stochastic claims reserving models assume independence between different accident years. Therefore, such models fail to model claims inflation appropriately, because claims inflation acts on all accident years simultaneously. We introduce a Bayes chain ladder reserving model which enables us to model claims inflation. In this model we derive analytical formulas for the posterior distribution, the claims reserves and their prediction uncertainty. Keywords Accounting year effects modeling Á Claims inflation Á Bayes chain ladder model Á Multivariate dependence modeling Á General insurance liabilities Á Outstanding loss liabilities Á Claims reserving Á Loss development

Calendar Year Effect Modeling for Claims Reserving in HGLM

“…In fact, the reserve in Table 2 is about 8% higher than that in Table 3 and even more relevant is the difference between the prediction errors, about 24% higher in Table 2. Actually, as noted in several papers (e.g., Wüthrich, 2010;Salzmann and Wüthrich, 2012;Bühlmann and Moriconi, 2015), the inclusion of random diagonal effects can be significant especially for the evaluation of the prediction uncertainty. The higher prediction errors are implied by a more appropriate dependence modeling of the incremental payments.…”

“…In this context, by assuming a Bayesian set-up, Wüthrich (2010) studies a Bayes CL model that allows for inference on calendar year random parameters. Within the same framework, Salzmann and Wüthrich (2012) define a multivariate Bayes CL model that enables modeling dependence along accounting years and study the sensitivities of claims reserves and prediction uncertainty as a function of a correlation parameter within accounting years. In the credibility framework, Bühlmann and Moriconi (2015) develop a stochastic claims reserving model that extends the Bühlmann-Straub claims reserving model.…”

A Power Law Extrapolation – Interpolation Method for IBNR Claims Reserving

“…For this reason, they fail to model claims inflation appropriately, because claims inflation acts on all accident years simultaneously. A model that accounts for accident year dependence in runoff triangles has been proposed by Salzmann and Wüthrich [18].…”

A Copula Regression for Modeling Multivariate Loss Triangles and Quantifying Reserving Variability

“…Despite the vast studies in the multivariate claims reserving, modeling the dependency among multiple triangles is still a challenge. Because of the timedependent evolution, correlation among payments could be introduced by various sources, among which the calendar year effect is the focus of the current literature (see, for example, Shi et al, 2012;Wüthrich, 2012;Salzmann and Wüthrich, 2012;Merz et al, 2013). Specifically, losses among triangles could be correlated due to a common calendar year effect, such as a court judgment or management decision, that could affect all open claims in the portfolio simultaneously.…”