Before revision:  We introduce a  class of dynamic risk measures  in terms of a certain family of g-expectations driven by Wiener and Poisson point processes . In analogy with the static case, we show that these risk measures, which we label dynamic spectral risk measures , are locally law-invariant and additive on the set of pathwise increasing random variables .
After revision:  We introduce a class of dynamic risk measures in terms of a certain family of g-expectations driven by Wiener and Poisson point processes , which we call dynamic spectral risk measures , are locally law-invariant and additive on the set of pathwise increasing random variables .