Lost in Translation: Explicitly Solving Nonlinear Stochastic Optimal Control Problems Using the Median Objective Value

Abstract

Policy makers constantly face optimal control problems: what controls allow them to achieve certain targets in, e.g., GDP growth or inflation? Conventionally this is done by applying certain linear-quadratic optimization algorithms to dynamic econometric models. Several algorithms extend this baseline framework to nonlinear stochastic problems. However, those algorithms are limited in a variety of ways including, most importantly, their restriction to local best solutions only and the symmetry of objective function. The contribution of the current study is that we adopt differential evolution (DE) in the context of nonlinear stochastic optimal control problems, thus ensuring better convergence to a global optimum and explicitly considering parameter uncertainty by evaluating the expected objective function. The latter is done by minimizing the median over a set of multiple Monte Carlo draws of uncertain parameters and by separately evaluating the random parameter draws looking particularly at extreme cases. Comparing DE with more traditional methods, which make use of linear-quadratic optimization, in two economic models, we find that the solutions obtained for expected and ex-post functions differ consistently raising doubts about the optimality of ex-post solutions. We claim that this research is aimed to broaden the range of decision support information used by policy makers when choosing an optimal strategy under much more realistic conditions.