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.

我们考虑了一个结合了依赖不确定性和关于依赖结构的附加信息的多资产期权的模型无关边界的计算。我们提供了在这种情况下的资产定价的基本定理，以及一个超对冲对偶性，可以将概率度量上的最大化问题转化为更易解的交易策略上的最小化问题。我们使用惩罚方法和人工神经网络的深度学习逼近来解决后者。数值方法快速，并且计算时间与交易资产的数量成线性比例。最后，我们检验了各种附加信息的重要性。经验证据表明，“相关”的信息，即与目标回报相同的衍生品价格，比其他信息更有用，并且应在精确性和计算效率之间的权衡中优先考虑。

利用期权隐含信息和深度学习改进的无模型多资产期权上限