  We introduce a new class of forward performance processes that are endogenous
and predictable with regards to an underlying market information set and,
furthermore, are updated at discrete times. We analyze in detail a binomial
model whose parameters are random and updated dynamically as the market
evolves. We show that the key step in the construction of the associated
predictable forward performance process is to solve a single-period inverse
investment problem, namely, to determine, period-by-period and conditionally on
the current market information, the end-time utility function from a given
initial-time value function. We reduce this inverse problem to solving a
functional equation and establish conditions for the existence and uniqueness
of its solutions in the class of inverse marginal functions.
