The superhedging price is a
coherent risk measure
In the fields of actuarial science and financial economics there are a number of ways that risk can be defined; to clarify the concept theoreticians have described a number of properties that a risk measure might or might not have. A coherent ris ...
. The superhedging price of a
portfolio
Portfolio may refer to:
Objects
* Portfolio (briefcase), a type of briefcase
Collections
* Portfolio (finance), a collection of assets held by an institution or a private individual
* Artist's portfolio, a sample of an artist's work or a c ...
(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
In economics, a complete market (aka Arrow-Debreu market or complete system of markets) is a market with two conditions:
# Negligible transaction costs and therefore also perfect information,
# there is a price for every asset in every possible st ...
the superhedging price is equivalent to the price for
hedging the initial portfolio.
Mathematical definition
If the set of
equivalent martingale measures is denoted by EMM then the superhedging price of a portfolio ''X'' is
where
is defined by
: