Robust control in the presence of a colored model error term in discrete time

By explicitly taking into account the welfare loss associated with the various controls, it has been recently shown that the usual, i.e. with white noise model error term, robust control framework in discrete time problems implies that both players (the controller and malevolent nature) optimize their objective functional by treating today's shock (either malevolent or not) as linearly uncorrelated to tomorrow's shock, see e.g. [38]. Therefore, by construction, the most common robust control framework implies that the game at time t is linearly uncorrelated with the game at time t + 1. It is then useless to handle situations characterized by correlated malevolent shocks. In this paper it is assumed that the standard robust control problem in discrete time with unstructured uncertainty à la Hansen and Sargent, i.e. a nonparametric set of additive mean-distorting model perturbations, where the decision maker is assumed to be “probabilistically sophisticated" is characterized by a colored model error (or system disturbance) term. The new ? -constrained worstcase controls for the decision maker and malevolent nature are derived. The e ect of this new assumption on the results of some well known models, like the permanent income model, is discussed.