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Intrinsic Risk Measures

28 Pages Posted: 9 Nov 2016 Last revised: 18 Nov 2016

Walter Farkas

University of Zurich, Swiss Finance Institute (SFI) at Department of Banking and Finance; ETH Zürich - Department of Mathematics; Swiss Finance Institute

Alexander Smirnow

University of Zurich - Department of Banking and Finance; ETH Zürich - Department of Mathematics

Date Written: October 26, 2016

Abstract

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.

Keywords: intrinsic risk measures, monetary risk measures, acceptance sets, coherence, conicity, quasi-convexity, value at risk

JEL Classification: C60, G11, G20

Suggested Citation

Farkas, Walter and Smirnow, Alexander, Intrinsic Risk Measures (October 26, 2016). Swiss Finance Institute Research Paper No. 16-65. Available at SSRN: https://ssrn.com/abstract=2866406 or http://dx.doi.org/10.2139/ssrn.2866406

Walter Farkas (Contact Author)

University of Zurich, Swiss Finance Institute (SFI) at Department of Banking and Finance ( email )

Plattenstrasse 14
CH-8032 Zurich, Zurich 8032
Switzerland
+41-44-634 3953 (Phone)
+41-44-634 4345 (Fax)

HOME PAGE: http://https://people.math.ethz.ch/~farkas/

ETH Zürich - Department of Mathematics ( email )

ETH Zentrum HG-F 42.1
Raemistr. 101
CH-8092 Zurich, 8092
Switzerland

HOME PAGE: http://https://people.math.ethz.ch/~farkas/

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Alexander Smirnow

University of Zurich - Department of Banking and Finance ( email )

Schönberggasse 1
Zürich, 8001
Switzerland

ETH Zürich - Department of Mathematics ( email )

ETH Zentrum HG-F 42.1
Raemistr. 101
CH-8092 Zurich, 8092
Switzerland

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