We introduce a new class of forward performance processes that are predictable with regards to an underlying filtration and are updated in discrete time. Such performance criteria may accommodate short-term predictability of asset returns, sequential learning and other dynamically unfolding factors affecting optimal portfolio choice. We analyze in detail a binomial model. We show that the key step is to solve a single-period inverse investment problem, which we study in detail. In particular, We reduce this inverse problem to an iterative (i.e. single variable) functional equation and establish conditions for existence and uniqueness of solutions in the class of inverse marginal functions. This functional equation is the counterpart of the stochastic partial differential equation that characterizes the continuous-time forward performance processes.
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