Bidual Representation of Expectiles

Alejandro Balbás (), Beatriz Balbás, Raquel Balbás and Jean-Philippe Charron
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Alejandro Balbás: Department of Business Administration, University Carlos III of Madrid, C/Madrid, 126, 28903 Getafe, Madrid, Spain
Beatriz Balbás: Department of Economics and Business Administration, University of Alcalá, Pl. de la Victoria, 2, 28802 Alcalá de Henares, Madrid, Spain
Raquel Balbás: Department of Financial and Actuarial Economics and Statistics, University Complutense of Madrid, Somosaguas, 28223 Pozuelo de Alarcón, Madrid, Spain
Jean-Philippe Charron: Department of Finance and Commercial Research, Autonomous University of Madrid, C/Francisco Tomás y Valiente, 5, 28049 Madrid, Spain

Risks, 2023, vol. 11, issue 12, 1-21

Abstract: Downside risk measures play a very interesting role in risk management problems. In particular, the value at risk (VaR) and the conditional value at risk (CVaR) have become very important instruments to address problems such as risk optimization, capital requirements, portfolio selection, pricing and hedging issues, risk transference, risk sharing, etc. In contrast, expectile risk measures are not as widely used, even though they are both coherent and elicitable. This paper addresses the bidual representation of expectiles in order to prove further important properties of these risk measures. Indeed, the bidual representation of expectiles enables us to estimate and optimize them by linear programming methods, deal with optimization problems involving expectile-linked constraints, relate expectiles with VaR and CVaR by means of both equalities and inequalities, give VaR and CVaR hyperbolic upper bounds beyond the level of confidence, and analyze whether co-monotonic additivity holds for expectiles. Illustrative applications are presented.

Keywords: VaR and CVaR; expectile; dual and bidual representations; risk optimization; risk bounds and equalities (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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