This paper introduces a novel technique for the consistent estimation of models described by restrictions on optimized conditional moments of state and control variables. The method is nonparametric with respect to the dynamics of these variables, and does not require data on the moment optimizer. The technique is illustrated in a financial application: the estimation of portfolio weights and other properties of the unobservable self-financing strategy that best replicates target cash-flows in a Markovian setting. In addition, the paper discusses how the technique can be employed for the estimation of other optimized functions of state and control variables that are of interest in economic applications, such as maximized expected individual intertemporal utilities in microeconomic models.