Although death occurs with certainty, the time of death is uncertain. In this paper we build on this conceptualization and show that, although life ends at some point in time, human life can be meaningfully conceptualized as a strive for immortality that is never reached. We consider an intertemporal problem where health investments and consumption choices are made, taking into account that mortality depends on environmental factors, which are not controlled by the agent, and the agent's health condition, which is endogenous to lifestyle and health behavior. Formally, the infinite horizon approach has the advantage that adjustment dynamics to the steady state (i.e. human aging) can be discussed analytically. We explore the determinants of health deficits in this framework and show how individuals choose consumption and health expenditure over their lifetime in order to slow down (biological) aging. We compute analytically the impulse response functions for unexpected parameter changes. Specifically, we investigate how higher prices for medical goods and advancing medical technology affect individual behavior and health deficit accumulation.