Stochastic Optimization Models in Finance || Consumption Decisions under Uncertainty**The research underlying this paper was initiated while the authors were both affiliated with the Graduate School of Industrial Administration, Carnegie-Mellon University; the support of that institution, and at a later stage of the Sloan School of Management, Massachussets Institute of Technology, is gratefully acknowledged. The authors also wish to thank Albert Ando and Ralph Beals for their helpful assistance at an early stage of this work, as well as Louis Gevers, Agnar Sandmo and Joseph Stiglitz for their critical reading of the final manuscript.