Premium indexing in lifelong health insurance

For lifelong health insurance covers, medical inflation not incorporated in the level premiums determined at policy issue requires an appropriate increase of these premiums and/or the corresponding reserves during the term of the contract. In this paper, we investigate appropriate premium indexing mechanisms, based on a given medical inflation index. First, we consider a general relation between benefit, premium and reserve increases, which can be used on a yearly basis
to restore the actuarial equivalence that is broken due to observed medical inflation over the past year. Next, we consider an individual premium indexing mechanism, depending on the age at policy issue, which makes the relative premium increases above the observed medical inflation more stable over time. Finally, we consider an aggregate premium indexing mechanism for a portfolio of new entrants, where the relative premium increase above the observed inflation is independent of age-at-entry, introducing intergenerational solidarity.