Bidual Approaches in Risk Representation

32 Pages Posted: 15 Jan 2021

See all articles by Alejandro Balbás

Alejandro Balbás

Universidad Carlos III de Madrid

Beatriz Balbás

University of Alcala

Raquel Balbás

Universidad Complutense de Madrid (UCM)

Date Written: November 9, 2020

Abstract

Downside and deviation risk measures are becoming more and more important in many disciplines with clear interfaces with Applied Mathematics and Operations Research. Their dual representations have played critical roles in most of their applications (risk management, portfolio selection, pricing and hedging, etc.), but, to the best of our knowledge, bidual representations were never profoundly studied. New linear bidual representations will be provided, and their great capacity to linearize many problems will be proved, with special focus on risk optimization. This is important because there are very tractable necessary and sufficient optimality conditions and resolution algorithms in Linear Programming. Moreover, in the linearization process, one will have to introduce new decision variables providing us with very important information, such as sensitivities with respect to the selected risk measure and sensitivities with respect to the selected model (model risk). The theory will be presented for general Banach spaces, and an illustrative example will be given.

Keywords: Risk Measure, Bidual Representation, Model Risk

JEL Classification: C61, G11, G22.

Suggested Citation

Balbás, Alejandro and Balbás, Beatriz and Balbás, Raquel, Bidual Approaches in Risk Representation (November 9, 2020). Available at SSRN: https://ssrn.com/abstract=3727433 or http://dx.doi.org/10.2139/ssrn.3727433

Alejandro Balbás (Contact Author)

Universidad Carlos III de Madrid ( email )

CL. de Madrid 126
Madrid, Madrid 28903
Spain

Beatriz Balbás

University of Alcala ( email )

Plaza de la Victoria, 2.
Alcala de Henares, Madrid 28801
Spain

Raquel Balbás

Universidad Complutense de Madrid (UCM)

Carretera de Humera s/n
Madrid, Madrid 28223
Spain

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