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. In a complete market the superhedging price is equivalent to the price for hedging the initial portfolio.
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Mathematical definition
If the set of equivalent martingale measures is denoted by EMM then the superhedging price of a portfolio X is
Acceptance set
The acceptance set for the superhedging price is the negative of the set of values of a self-financing portfolio at the terminal time. That is
Subhedging price
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. Mathematically it can be written as
Dynamic superhedging price
The dynamic superhedging price has conditional risk measures of the form:
where