We propose to derive deviation measures through the Minkowski gauge of a given set of acceptable positions. We show that  given a suitable acceptance set, any positive homogeneous deviation measure can be accommodated in our framework. In doing so, we provide a new interpretation for such measures, namely, that they quantify how much one must shrink  a position for it to become acceptable. In particular, the Minkowski gauge of a set which is convex, stable under scalar addition, and radially bounded at non-constants, is a generalized deviation measure. Furthermore, we explore the relations existing between mathematical and financial properties attributable to an acceptance set on the one hand , and the corresponding properties of the induced measure on the other . Dual characterizations in terms of polar sets and support functionals are provided.
We propose to derive deviation measures through the Minkowski gauge of a given set of acceptable positions. We show that , given a suitable acceptance set, any positive homogeneous deviation measure can be accommodated in our framework. In doing so, we provide a new interpretation for such measures, namely, that they quantify how much one must shrink or deleverage a position for it to become acceptable. In particular, the Minkowski Deviation of a set which is convex, stable under scalar addition, and radially bounded at non-constants, is a generalized deviation measure. Furthermore, we explore the relations existing between mathematical and financial properties attributable to an acceptance set , and the corresponding properties of the induced measure . Hence, we fill the gap that is the lack of an acceptance set for deviation measures . Dual characterizations in terms of polar sets and support functionals are provided.
A
,
A
or deleverage
R
gauge
Deviation
D
on the one hand
R
on the other
. Hence, we fill the gap that is the lack of an acceptance set for deviation measures