We consider the computation of model-free bounds for multi-asset options in a setting that combines dependence uncertainty with additional information on the dependence structure. More specifically, we consider the setting where the marginal distributions are known and partial information, in the form of known prices for multi-asset options, is also available in the market. We provide a fundamental theorem of asset pricing in this setting, as well as a superhedging duality that allows to transform the maximization problem over probability measures in a more tractable minimization problem over trading strategies. The latter is solved using a penalization approach combined with a deep learning approximation using artificial neural networks. The numerical method is fast and the computational time scales linearly with respect to the number of traded assets. We finally examine the significance of various pieces of additional information. Empirical evidence suggests that "relevant" information, i.e. prices of derivatives with the same payoff structure as the target payoff, are more useful that other information, and should be prioritized in view of the trade-off between accuracy and computational efficiency.

翻译：我们考虑在依赖结构不确定性与附加依赖结构信息相结合的设定下，计算多资产期权的无模型边界。具体而言，我们研究边际分布已知且市场中存在多资产期权已知价格形式的部分信息的情形。我们在此设定下提出了资产定价基本定理，以及一种超对冲对偶性，该对偶性可将概率测度上的最大化问题转化为交易策略上更易处理的最小化问题。后者通过惩罚方法结合使用人工神经网络的深度学习近似求解。该数值方法计算速度快，且计算时间与交易资产数量呈线性关系。最后，我们检验了各类附加信息的重要性。实证证据表明，“相关”信息（即具有与目标收益相同收益结构的衍生品价格）比其他信息更有用，在考虑精度与计算效率之间的权衡时，应优先使用此类信息。