DYNAMIC OPTIMIZATION WITHOUT DYNAMIC-PROGRAMMING

To solve a multiperiod optimization problem with a differentiable and concave objective function and a differentiable function for the dynamic process, this paper suggests an alternative to dynamic programming. It extends the method of Lagrange multipliers and Pontryagin's maximum principle to the stochastic case and proposes to solve for a Lagrangian function rather than the value function in dynamic programming. Since the value function is a solution to the partial differential equations given by the Lagrange functions, the method proposed is analytically simpler and computationally more efficient. Numerical methods of optimization using Lagrange multipliers and an illustrative example from the study of real business cycles are provided.