Parametric Phi-Divergence-Based Distributionally Robust Optimization for Insurance Pricing

Sliwinski, Lukasz and Llamazares-Elias, Liam and Siska, David and Szpruch, Lukasz (2025) Parametric Phi-Divergence-Based Distributionally Robust Optimization for Insurance Pricing. In: Proceedings of the 6th ACM International Conference on AI in Finance :. ACM, New York, pp. 378-386. ISBN 9798400722202

Abstract

This paper investigates the use of φ -divergence-based distributionally robust optimization (φ -DRO) for offline insurance pricing. To this end, we introduce a parametric formulation of DRO where the uncertainty follows a known parametric model. We interpret φ -divergence-based DRO as the optimization of a risk functional over the objective distribution, offering an intuitive understanding of its behaviour. Applying this framework to a real-world-inspired insurance pricing problem, we find that the obtained robust policies tend to be overly conservative and yield limited performance gains under distributional shifts. These findings are validated through experiments in both the insurance pricing domain and a synthetic pricing environment. Our results suggest that while φ -DRO provides theoretical robustness, its practical benefits in offline pricing may be limited in certain problems.