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Lifelong Health Insurance Covers with Surrender Values: Updating Mechanisms in the Presence of Medical Inflation

For lifelong health insurance covers, medical inflation not sufficiently incorporated in the level premiums determined at policy issue requires an appropriate increase of these premiums and/or of the corresponding reserves during the term of the contract. This premium and/or reserve update is necessary to maintain the actuarial equivalence between future health benefits and withdrawal payments on the one hand, and available reserves and future premiums on the other hand. In Vercruysse et al. (2013), premium and reserve indexing mechanisms were proposed in a discrete-time framework where medical inflation is only taken into account expost as it emerges over time and where the reserves are not transferable in case of policy cancellation. In this paper, we extend this work by investigating the more general situation where a surrender value is paid out in case of policy cancellation. Reserve-based as well as premium-based surrender values are considered.