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 , and letting be the Lp space in the scalar case and in d-dimensions, then we can define acceptance sets as below.
An acceptance set is a set satisfying:
An acceptance set (in a space with assets) is a set satisfying:
Additionally, if is convex (a convex cone) then it is called a convex (coherent) acceptance set. [2]
Note that where is a constant solvency cone and is the set of portfolios of the reference assets.
An acceptance set is convex (coherent) if and only if the corresponding risk measure is convex (coherent). As defined below it can be shown that and .[ 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. That is
where is the exponential utility function. [3]
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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 , and letting be the Lp space in the scalar case and in d-dimensions, then we can define acceptance sets as below.
An acceptance set is a set satisfying:
An acceptance set (in a space with assets) is a set satisfying:
Additionally, if is convex (a convex cone) then it is called a convex (coherent) acceptance set. [2]
Note that where is a constant solvency cone and is the set of portfolios of the reference assets.
An acceptance set is convex (coherent) if and only if the corresponding risk measure is convex (coherent). As defined below it can be shown that and .[ 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. That is
where is the exponential utility function. [3]
{{
cite journal}}
: Cite journal requires |journal=
(
help)