Spectral Martingale Measures

We show that given a class of comonotonic claims there is a probability measure Q such that the dynamic spectral risk measure of each such claim is a martingale under Q. The applications explored of this result are: (1) the use of statistical and calibration techniques that are typically employed under the law of one price, such as digital moment estimation and fast Fourier transform; (2) a simplified numerical scheme for the nonlinear valuation of financial claims and of portfolio selection that minimizes the worst case scenario value; (3) the definition of a dynamic, time-consistent, convex, but not coherent spectral risk measure, which allows the introduction of diminishing marginal returns without the theoretical limitations of expected utility theory