Conditional generalized quantiles based on expected utility model and equivalent characterization of properties

TL;DR

This paper introduces conditional generalized quantiles as a new class of risk measures, characterizes their properties and coherence, and explores their time consistency for dynamic risk assessment.

Contribution

It proposes a novel conditional risk measure based on generalized quantiles, providing equivalent characterizations and analyzing their properties and time consistency.

Findings

Well-definedness of conditional generalized quantiles

Characterization of coherence and convexity

Time consistency properties established

Abstract

As a counterpart to the (static) risk measures of generalized quantiles and motivated by Bellini et al. (2018), we propose a new kind of conditional risk measure called conditional generalized quantiles. We first show their well-definedness and they can be equivalently characterised by a conditional first order condition. We also discuss their main properties, and, especially, We give the characterization of coherency/convexity. For potential applications as a dynamic risk measure, we study their time consistency properties, and establish their equivalent characterizations among conditional generalized quantiles.