  We show that pointwise limits of semistatic trading strategies in discrete
time are again semistatic strategies. The analysis is carried out in full
generality for a two-period model, and under a probabilistic condition for
multi-period, multi-stock models. Our result contrasts with a counterexample of
Acciaio, Larsson and Schachermayer, and shows that their observation is due to
a failure of integrability rather than instability of the semistatic form.
Mathematically, our results relate to the decomposability of functions as
studied in the context of Schr\"odinger bridges.
