This paper studies the problem of updating the super-replication prices of an arbitrage-free market in a multiperiod setting. We introduce a set of standard properties and a (weak) version of Dynamic Consistency to characterize the updated pricing rules by the Full Bayesian Rule. Since different pricing rules are related to different kinds of frictions on the financial markets, this study allow us to analyze the evolution of the market structure when new informations are revealed. We also provide a geometric characterization for the pricing rules that characterizes frictionless incomplete markets. This geometric property is useful to demonstrate that the incomplete frictionless market structure is invariant under updating when a non trivial updating condition between the set of risk-neutral measures and revealed information is present.