RT Journal Article
T1 Bidual representation of expectiles
A1 Balbás De La Corte, Alejandro
A1 Balbás, Beatriz
A1 Balbás Aparicio, Raquel
A1 Charron, Jean-Philippe
AB 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.
PB MDPI
YR 2023
FD 2023
LK https://hdl.handle.net/20.500.14352/105769
UL https://hdl.handle.net/20.500.14352/105769
LA eng
NO Risks 2023, 11(12), 220; https://doi.org/10.3390/risks11120220
NO 2023 descuento MDPI
NO Ministerio de Ciencia e Innovación (España)
NO Universidad Carlos III de Madrid
DS Docta Complutense
RD 9 abr 2025