Financing innovative and costly treatments in various therapeutic fields entails a number of problems in countries where costs are covered by public services. Providing these drugs is forcing actors to define the maximum sums of money society is willing to spend for given health improvements. This raises the question of whether maximum financing should vary according individuals' circumstances, such as the rareness of a disease, lifestyles, social inequalities experienced over a life time, etc. This article examines a particular priority, namely that given to the youngest patients, such prioritising usually refers to the "fair innings argument" (FIA). The challenge is to identify if, and on the basis of what arguments, collective choices should take into account age in the name of a right to live the time required for a complete life, within a context of the scarcity of resources and the pluralism of values. Three arguments are considered. At first we consider that FIA could be justified by the objective of equalizing the opportunities of well-being. Next, we proposed justifying the fair innings argument with the aim of equalizing the time provided to individuals to achieve their plan of life, in accordance with Rawls's theory of justice as fairness. Finally, we proposed considering the FIA as being justified because of the goal of equalizing the time provided to individuals to accept death. These three arguments, of course, have many limitations, some of which we have highlighted.