Mean and variance optimization of non–linear systems and worst–case analysis

In this paper, we consider expected value, variance and worst–case optimization of nonlinear models. We present algorithms for computing optimal expected value, and variance policies, based on iterative Taylor expansions. We establish convergence and consider the relative merits of policies based on expected value optimization and worst–case robustness. The latter is a minimax strategy and ensures optimal cover in view of the worst–case scenario(s) while the former is optimal expected performance in a stochastic setting. Both approaches are used with a small macroeconomic model to illustrate relative performance, robustness and trade-offs between the alternative policies.