Before revision:  Under a suitable scaling of the probability distortions and provided that the tick-size and time step-size converge to zero in such a way that the multinomial random walks converge to a Levy process , we show that values of random variables under the multi-period distorted expectations converge to the values under a continuous-time non-linear expectation operator, which may be identified with a certain type of Peng's g-expectation. A coupling argument is given to show that this operator reduces to a classical linear expectation when restricted to the set of pathwise increasing claims.
After revision:  Under a suitable scaling of the probability distortions and provided that the tick-size and time step-size converge to zero in such a way that the multinomial random walks converge to a Levy process , 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 claims.