Before revision:  This involves a certain non-standard scaling of the corresponding spectral weight-measures that we identify explicitly  .
After revision:  This involves a certain non-standard scaling of the corresponding spectral weight-measures that we identify explicitly . We also define a family of market-consistent dynamic spectral risk measures in the setting of a financial market. We identify the corresponding optimal hedging strategy and show that the negative of the value of such a risk measure is equal to the smallest price under a certain family of equivalent martingale measures. By varying the parameters of the risk measure we show that this price ranges between the subhedging price and the price under the minimal martingale measure .