This paper offers a theoretical investigation of long term coverage of health risks. I focus upon two key features in a long term perspective: first, individuals bear the risk that their risk category may change through time; second, in the long run, uncertainty may be "radical", i.e., difficult to probabilise. After briefly summarising the dynamic elements of theories of solidarity (according to Leon Bourgeois and John Rawls), the second part presents recent economic approaches of long term risk management, and reviews the solutions that have been offered in the area of health care. The third part attempts to apply these solutions to the French health insurance system made of two parts: mandatory public insurance, and private supplementary insurance, regulated by the Loi Evin. Lastly, the final section offers a first examination, both theoretical and descriptive, of the comparative advantages of mutuals (non profit) and insurance companies (for profit), two forms of private institutions involved in health insurance, focusing on the long term aspects of this activity. The conclusion insists on the limits of the analysis, and suggests paths for future research. [Authors]