Characterization of optimal plans for stochastic dynamic programs

This paper provides general techniques for the characterization of optimal plans resulting from stochastic dynamic programming. We show that under standard assumptions the optimal plans in both finite and infinite horizon problems can be obtained by an application of the Implicit Function Theorem to first order conditions. Further, we show that under certain checkable conditions, optimal plans and value functions are p-times differentiable for any integer p [ges] 0. Finally, we apply our technique to obtain a Cp plan and value function in a one sector infinite horizon growth problem under uncertainty.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/23779/1/0000017.pd