  Motivated by the model- independent pricing of derivatives calibrated to the
real market, we consider an optimization problem similar to the optimal
Skorokhod embedding problem, where the embedded Brownian motion needs only to
reproduce a finite number of prices of Vanilla options. We derive in this paper
the corresponding dualities and the geometric characterization of optimizers.
Then we show a stability result, i.e. when more and more Vanilla options are
given, the optimization problem converges to an optimal Skorokhod embedding
problem, which constitutes the basis of the numerical computation in practice.
In addition, by means of different metrics on the space of probability
measures, a convergence rate analysis is provided under suitable conditions.
