Before revision:  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. We substantiate the link between dynamic spectral risk measures and their static counterparts by establishing a limit theorem for general path-functionals which shows that such dynamic risk measures arise as limits under vanishing time-step of iterated spectral risk measures driven by approximating lattice random walks.
After revision:  We introduce a new class of dynamic risk measures given in terms of certain backward stochastic differential equations. By establishing a functional limit theorem, we show that DSRs may be considered to be (strongly) time-consistent continuous-time extensions of iterated spectral risk measures driven by approximating lattice random walks.