Seven Proofs for the Subadditivity of Expected Shortfall

• Autorzy: Paul Embrechts , Ruodu Wang
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Expected Shortfall; TVaR; subadditivity; comonotonicity; Value-at-Risk; risk management; education

Kategorie tematyczne

• 91B06: Decision theory
• 60E15: Inequalities; stochastic orderings
• 28A25: Integration with respect to measures and other set functions

• Wydawca: De Gruyter Open
• Czasopismo: Dependence Modeling
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2015-08-15

zaakceptowano

2015-10-07

online

2015-10-16

Twórcy

autor

Paul Embrechts

• RiskLab, Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland

autor

Ruodu Wang

• Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON
  N2L 3G1, Canada

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Identyfikatory

DOI

10.1515/demo-2015-0009