This paper introduces a technique for the consistent estimation of optimized functions of state and control variables and a class of their functionals. The technique is illustrated in an application to a Markovian model for self-financing portfolio strategies with payoffs with nonparametric dynamics. The focus is on the strategies that best replicate target cash-flows on the basis of expected square replication errors, and the novel technique estimates the optimal weights and the dispersion of the payoffs of the optimal strategies. 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.

(This is a single-authored paper)