In financial mathematics, acceptance set is a set of acceptable future net worth which is acceptable to the regulator.
It is related to risk measures.
Given a probability space
be the Lp space in the scalar case and
in d-dimensions, then we can define acceptance sets as below.
satisfying: An acceptance set (in a space with
satisfying: Additionally, if
is convex (a convex cone) then it is called a convex (coherent) acceptance set.
is a constant solvency cone and
reference assets.
An acceptance set is convex (coherent) if and only if the corresponding risk measure is convex (coherent).
[citation needed] The acceptance set associated with the superhedging price is the negative of the set of values of a self-financing portfolio at the terminal time.
That is The acceptance set associated with the entropic risk measure is the set of payoffs with positive expected utility.
is the exponential utility function.