Journal article
Seven Proofs for the Subadditivity of Expected Shortfall
- Embrechts, Paul 1RiskLab, Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland
- Wang, Ruodu 2Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada
Published in:
- Dependence Modeling. - Walter de Gruyter GmbH. - 2015, vol. 3, no. 1
English
Abstract Subadditivity is the key property which distinguishes the popular risk measures Value-at-Risk and
Expected Shortfall (ES). In this paper we offer seven proofs of the subadditivity of ES, some found in the literature
and some not. One of the main objectives of this paper is to provide a general guideline for instructors
to teach the subadditivity of ES in a course. We discuss the merits and suggest appropriate contexts for each
proof.With different proofs, different important properties of ES are revealed, such as its dual representation,
optimization properties, continuity, consistency with convex order, and natural estimators.
Expected Shortfall (ES). In this paper we offer seven proofs of the subadditivity of ES, some found in the literature
and some not. One of the main objectives of this paper is to provide a general guideline for instructors
to teach the subadditivity of ES in a course. We discuss the merits and suggest appropriate contexts for each
proof.With different proofs, different important properties of ES are revealed, such as its dual representation,
optimization properties, continuity, consistency with convex order, and natural estimators.
- Language
-
- English
- Open access status
- gold
- Identifiers
-
- DOI 10.1515/demo-2015-0009
- ISSN 2300-2298
- Persistent URL
- https://sonar.ch/global/documents/66550
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