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

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