  Monetary risk measures are usually interpreted as the smallest amount of
external capital that must be added to a financial position to make it
acceptable. We propose a new concept: intrinsic risk measures and argue that
this approach provides a direct path from unacceptable positions towards the
acceptance set. Intrinsic risk measures use only internal resources and return
the smallest percentage of the currently held financial position which has to
be sold and reinvested into an eligible asset such that the resulting position
becomes acceptable. While avoiding the problem of infinite values, intrinsic
risk measures allow a free choice of the eligible asset and they preserve
desired properties such as monotonicity and quasi-convexity. A dual
representation on convex acceptance sets is derived and the link of intrinsic
risk measures to their monetary counterparts on cones is detailed.
