To report or not to report: Optimal claim reporting in a bonus-malus system
Abstract
We study an optimal claim reporting problem in a bonus-malus setting. We assume, that the insurance contract consists of two regimes, where reporting a claim leads to a transition to a higher-premium regime, whereas remaining claim-free for a prespecified time period results in a shift to the lower premium regime. The insured can decide whether or not to report an occurred claim. We formulate this as an optimal control problem, where the policyholder follows a barrier-type reporting strategy, with the goal of maximizing the expected value of a function of their terminal wealth. We show that the associated value function is the unique viscosity solution to a system of Hamilton-Jacobi-Bellman equations. This characterization allows us to compute numerical approximations of the optimal barrier strategies.
Keywords
Cite
@article{arxiv.2601.07655,
title = {To report or not to report: Optimal claim reporting in a bonus-malus system},
author = {Lea Enzi and Stefan Thonhauser},
journal= {arXiv preprint arXiv:2601.07655},
year = {2026}
}