Person:
Balbás De La Corte, Alejandro

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First Name
Alejandro
Last Name
Balbás De La Corte
URI
https://hdl.handle.net/20.500.14352/82727
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Económicas y Empresariales
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Area
Economía Financiera y Contabilidad
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Author: Balbás De La Corte, Alejandro × Subject: 33 ×

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    Bidual representation of expectiles
    (Risks, 2023) Balbás De La Corte, Alejandro; Balbás, Beatriz; Balbás Aparicio, Raquel; Charron, Jean-Philippe
    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.