Before revision: In this paper we explore a novel way to combine the dynamic notion of time-consistency with the static notion of quantile-based coherent risk measure or spectral risk measure, of which Expected Shortfall is a prime example. We introduce a new class of dynamic risk measures given in terms of a certain family of g-expectations driven by Wiener and Poisson point processes, which we call dynamic spectral risk measures.
After revision: In this paper we propose the notion of continuous-time dynamic spectral risk-measure (DSR). Adopting a Poisson random measure setting, we define this class of dynamic risk measures given in terms of a certain family of g-expectations driven by Wiener and Poisson point processes, which we call dynamic spectral risk measures.