We study conditional expectiles, defined as a natural generalisation of conditional expectations by means of the minimisation of an asymmetric quadratic loss function. We show that conditional expectiles can be equivalently characterised by a conditional first order condition and we derive their main properties. For possible applications as dynamic risk measures, we discuss their time consistency properties.

Conditional expectiles, time consistency and mixture convexity properties / F. Bellini, V. Bignozzi, G. Puccetti. - In: INSURANCE MATHEMATICS & ECONOMICS. - ISSN 0167-6687. - 82(2018), pp. 117-123.

Conditional expectiles, time consistency and mixture convexity properties

G. Puccetti
2018

Abstract

We study conditional expectiles, defined as a natural generalisation of conditional expectations by means of the minimisation of an asymmetric quadratic loss function. We show that conditional expectiles can be equivalently characterised by a conditional first order condition and we derive their main properties. For possible applications as dynamic risk measures, we discuss their time consistency properties.
Conditional expectiles; Dynamic risk measures; Mixture concavity; Time consistency; Sequential consistency; Supermartingale property;
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
Settore SECS-S/01 - Statistica
Settore MAT/06 - Probabilita' e Statistica Matematica
2018
https://doi.org/10.1016/j.insmatheco.2018.07.001
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/589360
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