Before revision:  It is well known from the typical example, the superhedging risk measure in markets with transaction costs (expressed in the cash asset) as in Jouini and Kallal (1995), Roux and Zastawniak (2016), and Loehne and Rudloff (2014), that the usual scalar concept of time consistency is too strong and not satisfied.
After revision:  It is well known from the typical example, the superhedging risk measure in markets with transaction costs , as in Jouini and Kallal (1995), Roux and Zastawniak (2016), and Loehne and Rudloff (2014), that the usual scalar concept of time consistency is too strong and not satisfied.