Mean–Variance optimization in discrete-time decision processes with general utility function

We study general discrete-time Mean–Variance problems in a non-Markovian setting. The utility is a general, continuous function which may depend on the entire history of the process. It contains many recursive utility functions with non-linear aggregator as special cases. Under some continuity and compactness assumptions on the model data, we establish the existence of persistently optimal deterministic policies. For finite horizon problems this also yields a recursive solution algorithm. The theory which we develop here goes beyond Mean–Variance models and may be applied, e.g., to Optimized Certainty Equivalents. The Mean–Variance optimization framework is also applied to a multi-stage portfolio analysis with constraints on short selling.