Improved bounds on the copula of a bivariate random vector are computed when partial information is available, such as the values of the copula on a given subset of [0, 1]2, or the value of a functional of the copula, monotone with respect to the concordance order. These results are then used to compute model-free bounds on the prices of two-asset options which make use of extra information about the dependence structure, such as the price of another two-asset option.
"Improved Fréchet bounds and model-free pricing of multi-asset options." J. Appl. Probab. 48 (2) 389 - 403, June 2011. https://doi.org/10.1239/jap/1308662634