The superhedging price is a coherent risk measure.
The superhedging price of a portfolio (A) is equivalent to the smallest amount necessary to be paid for an admissible portfolio (B) at the current time so that at some specified future time the value of B is at least as great as A.
[1] If the set of equivalent martingale measures is denoted by EMM then the superhedging price of a portfolio X is
That is The subhedging price is the greatest value that can be paid so that in any possible situation at the specified future time you have a second portfolio worth less or equal to the initial one.
In a complete market then the supremum and infimum are equal to each other and a unique hedging price exists.
[4][5] The dynamic superhedging price has conditional risk measures of the form: where
It is a widely shown result that this is time consistent.