To report or not to report: Optimal claim reporting in a bonus-malus system
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912818429689856 |
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| author | Enzi, Lea Thonhauser, Stefan |
| author_facet | Enzi, Lea Thonhauser, Stefan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07655 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | To report or not to report: Optimal claim reporting in a bonus-malus system Enzi, Lea Thonhauser, Stefan Optimization and Control 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. |
| title | To report or not to report: Optimal claim reporting in a bonus-malus system |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2601.07655 |