Fitting Insurance Claim Reserves with Two-Way ANOVA and Intuitionistic Fuzzy Regression

Abstract

A highly relevant topic in the actuarial literature is so-called “claim reserving” or “loss reserving”, which involves estimating reserves to be provisioned for pending claims, as they can be deferred over various periods. This explains the proliferation of methods that aim to estimate these reserves and their variability. Regression methods are widely used in this setting. If we model error terms as random variables, the variability of provisions can consequently be modelled stochastically. The use of fuzzy regression methods also allows modelling uncertainty for reserve values using tools from the theory of fuzzy subsets. This study follows this second approach and proposes projecting claim reserves using a generalization of fuzzy numbers (FNs), so-called intuitionistic fuzzy numbers (IFNs), through the use of intuitionistic fuzzy regression. While FNs allow epistemic uncertainty to be considered in variable estimation, IFNs add bipolarity to the analysis by incorporating both positive and negative information regarding actuarial variables. Our analysis is grounded in the ANOVA two-way framework, which is adapted to the use of intuitionistic regression. Similarly, we compare our results with those obtained using deterministic and stochastic chain-ladder methods and those obtained using two-way statistical ANOVA.