Innovations in Insurance, Risk- and Asset Management

Abstract

The common risk measure classifies a financial position by the minimal amount of external capital that must be added to the position to make it acceptable.We introduce a new concept: intrinsic risk measures, which provide a more direct path from unacceptable positions towards the acceptance set. External capital is avoided and only internal resources are used. An intrinsic risk measure is defined by the smallest percentage of the currently held financial position which has to be sold and reinvested in an eligible asset such that the resulting position becomes acceptable. We show that this approach requires less investment in the eligible asset to arrive at acceptable positions. It evades the problem of infinite values while desired properties such as monotonicity and quasi-convexity are preserved. We derive a representation on cones and a dual representation on convex acceptance sets and we detail the connections of intrinsic risk measures to their monetary counterparts.