As the market has been free since 2006, some insurers are refraining from underwriting risks they deem to be over-exposed in spite of the obligation of motor insurance liability. The Direction des Assurances et de la Prévoyance Sociale (DAPS) will soon provide this type of risk with price-fixing tool that would prevent any excessive rating practiced by insurance companies.
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[3] https://www.atlas-mag.net/en/issue/lobbying-the-reinsurance-g10