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Conditional expectiles, time consistency and mixture convexity properties

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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… Click to show full 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.

Keywords: consistency mixture; time consistency; conditional expectiles; expectiles time

Journal Title: Insurance: Mathematics and Economics
Year Published: 2018

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