Gini Score under Ties and Case Weights

The Gini score is a popular tool in statistical modeling and machine learning for model validation and model selection. It is a purely rank based score that allows one to assess risk rankings. The Gini score for statistical modeling has mainly been used in a binary context, in which it has many equivalent reformulations such as the receiver operating characteristic (ROC) or the area under the curve (AUC). In the actuarial literature, this rank based score for binary responses has been extended to general real-valued random variables using Lorenz curves and concentration curves. While these initial concepts assume that the risk ranking is generated by a continuous distribution function, we discuss in this paper how the Gini score can be used in the case of ties in the risk ranking. Moreover, we adapt the Gini score to the common actuarial situation of having case weights.

Gini-based Model Monitoring: A General Framework with an Application to Non-life Insurance Pricing

In a dynamic landscape where portfolios and environments evolve, maintaining the accuracy of pricing models is critical. To the best of our knowledge, this is the first study to systematically examine concept drift in non-life insurance pricing. We (i) provide an overview of the relevant literature and commonly used methodologies, clarify the distinction between virtual drift and concept drift, and explain their implications for long-run model performance; (ii) review and formalize common performance measures, including the Gini index and deviance loss, and articulate their interpretation; (iii) derive the asymptotic distribution of the Gini index, enabling valid inference and hypothesis testing; and (iv) present a standardized monitoring procedure that indicates when refitting is warranted. We illustrate the framework using a modified real-world portfolio with induced concept drift and discuss practical considerations and pitfalls.

Enhancing Actuarial Non-Life Pricing Models via Transformers

Currently, there is a lot of research in the field of neural networks for non-life insurance pricing. The usual goal is to improve the predictive power via neural networks while building upon the generalized linear model, which is the current industry standard. Our paper contributes to this current journey via novel methods to enhance actuarial non-life models with transformer models for tabular data. We build here upon the foundation laid out by the combined actuarial neural network as well as the localGLMnet and enhance those models via the feature tokenizer transformer. The manuscript demonstrates the performance of the proposed methods on a real-world claim frequency dataset and compares them with several benchmark models such as generalized linear models, feed-forward neural networks, combined actuarial neural networks, LocalGLMnet, and pure feature tokenizer transformer. The paper shows that the new methods can achieve better results than the benchmark models while preserving certain generalized linear model advantages. The paper also discusses the practical implications and challenges of applying transformer models in actuarial settings.