Martingale conditions for optimal saving: discrete time

Necessary and sufficient conditions are derived for optimal saving in a stochastic neo-classical one-good world with discrete time. The usual technique of dynamic programming is replaced by classical variational and concavity arguments, modified to take account of conditions of measurability which represent the planner's information structure. Familiar conditions of optimality are thus extended to amit production risks represented by quite general random processes - no i.i.d.r.v.s., stationarity or Markov dependence are assumed - while utility and length of life also may be taken as random. It is found that the 'Euler' conditions may be interpreted as martingale properties of shadow prices