Optimal Aging with Uncertain Death

This note extends the theory of optimal aging and death (Dalgaard and Strulik, 2010) towards uncertain death. Specifically, it is assumed that at any age the probability to survive depends on the number of health deficits accumulated. It is shown that the results in Dalgaard and Strulik (2011) on the foundation of the Preston curve (the association between income and life-expectancy across countries) are robust against this extension. While results virtually coincide at high income levels, the stochastic version predicts somewhat more curvature of the Preston curve at low income levels. Taking uncertain death and a precautionary motive for health investment into account thus further improves a bit the anyway good fit of the Preston curve.