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.
Bellini, F., Bignozzi, V., & Puccetti, G. (2018). Conditional expectiles, time consistency and mixture convexity properties. INSURANCE MATHEMATICS & ECONOMICS, 82, 117-123 [10.1016/j.insmatheco.2018.07.001].
Conditional expectiles, time consistency and mixture convexity properties
Bellini, F;Bignozzi, V
;
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.
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