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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