Conditional Expectiles, Time Consistency and Mixture Convexity Properties
16 Pages Posted: 28 Jul 2017 Last revised: 21 Jul 2018
Date Written: July 11, 2018
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.
Keywords: Conditional expectiles, dynamic risk measures, mixture concavity, time consistency, sequential consistency, supermartingale property
JEL Classification: D81
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