Index insurance under demand and solvency constraints[Assurance indicielle sous contraintes de demande et de solvabilité]

Index insurance is often proposed to reduce protection gaps, especially for emerging risks. Unlike traditional insurance, it bases compensation on a measurable index, enabling faster payouts and lower claim management costs. This approach benefits both policyholders, through quick payments, and insurers, through reduced costs and better risk control due to reliable data and robust statistical estimates. An important difference with the concept of Cat Bonds is that the feasibility of such coverage relies on the possibility of mutualization. Mutualization, in turn, is achieved only if a sufficiently high number of policyholders agree to subscribe. The purpose of this paper is to introduce a model for the demand for index insurance and to provide conditions under which the solvency of the portfolio is achieved. From these conditions, we deduce a product that combines index and traditional indemnity insurance in order to benefit from the best of both approaches.