Conditional Expectiles, Time Consistency and Mixture Convexity Properties

16 Pages Posted: 28 Jul 2017 Last revised: 21 Jul 2018

See all articles by Fabio Bellini

Fabio Bellini

University of Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi

Valeria Bignozzi

Università di Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi

Giovanni Puccetti

University of Milan - Department of Economics, Management and Quantitative Methods (DEMM)

Date Written: July 11, 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.

Keywords: Conditional expectiles, dynamic risk measures, mixture concavity, time consistency, sequential consistency, supermartingale property

JEL Classification: D81

Suggested Citation

Bellini, Fabio and Bignozzi, Valeria and Puccetti, Giovanni, Conditional Expectiles, Time Consistency and Mixture Convexity Properties (July 11, 2018). Insurance: Mathematics and Economics, Forthcoming, Available at SSRN: https://ssrn.com/abstract=3009354 or http://dx.doi.org/10.2139/ssrn.3009354

Fabio Bellini

University of Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi ( email )

Milano, Milan
Italy

Valeria Bignozzi (Contact Author)

Università di Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi ( email )

Via Bicocca degli Arcimboldi, 8
Milano, 20126
Italy

Giovanni Puccetti

University of Milan - Department of Economics, Management and Quantitative Methods (DEMM) ( email )

Via Conservatorio, 7
Milan, 20122
Italy

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