Before revision:  We show that weakening the acceptability constraint leads to a shrinking bid-ask spread while considering model ambiguity makes the bid-ask spread even larger. Some algorithms and numerical examples are presented .
After revision:  Given this model, optimal bid and ask prices can be found by stochastic optimization. However, the model for the underlying asset price process is typically based on data and found by a nonparametric statistical estimation procedure. We define a confidence set of possible estimated models by a nonparametric neighborhood of a baseline model. This neighborhood serves as ambiguity set for a stochastic optimization problem under model uncertainty. We obtain distributionally robust solutions of the acceptability pricing problem and derive the dual problem formulation. Moreover, we relate the bid and ask prices under model ambiguity to the quality of the observed data .