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.

翻译：作为（静态）广义分位数风险测度的对应物，受 Bellini 等人 (2018) 的启发，我们提出了一种新型条件风险测度——条件广义分位数。我们首先证明了其良定义性，并表明它们可以通过条件一阶条件进行等价刻画。我们还讨论了其主要性质，特别是给出了其一致性/凸性的刻画。鉴于其作为动态风险测度的潜在应用，我们研究了其时间一致性性质，并建立了条件广义分位数之间时间一致性的等价刻画。