In this work, we consider optimal stopping problems with model uncertainty incorporated into the formulation of the underlying objective function. Typically, the robust, efficient hedging of American options in incomplete markets may be described as optimal stopping of such kind. Based on a generalisation of the additive dual representation of Rogers (Math. Financ. 12:271–286, 2002) to the case of optimal stopping under model uncertainty, we develop a novel regression-based Monte Carlo algorithm for the approximation of the corresponding value function. The algorithm involves optimising a penalised empirical dual objective functional over a class of martingales. This formulation allows us to construct upper bounds for the optimal value with reduced complexity. Finally, we carry out a convergence analysis of the proposed algorithm and illustrate its performance by several numerical examples.

在这项工作中，我们考虑将模型不确定性纳入基础目标函数的公式中的最优停止问题。通常，在不完全市场中对美式期权进行稳健、有效的对冲可被描述为此类最佳止损。基于 Rogers (Math. Financ. 12:271–286, 2002) 的加性对偶表示对模型不确定性下最优停止情况的推广，我们开发了一种新的基于回归的蒙特卡罗算法，用于近似对应的价值函数。该算法涉及优化一类鞅的惩罚经验双目标函数。这个公式使我们能够以降低的复杂性构建最优值的上限。最后，