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  1. Abstract 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 multiperiod, multistock 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 Schrödinger bridges. 
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