Standard rare-event simulation techniques require exact distributional specifications, which limits their effectiveness in the presence of distributional uncertainty. To address this, we develop a novel framework for estimating rare-event probabilities subject to such distributional model risk. Specifically, we focus on computing worst-case rare-event probabilities, defined as a distributionally robust bound against a Wasserstein ambiguity set centered at a specific nominal distribution. By exploiting a dual characterization of this bound, we propose Distributionally Robust Importance Sampling (DRIS), a computationally tractable methodology designed to substantially reduce the variance associated with estimating the dual components. The proposed method is simple to implement and requires low sampling costs. Most importantly, it achieves vanishing relative error, the strongest efficiency guarantee that is notoriously difficult to establish in rare-event simulation. Our numerical studies confirm the superior performance of DRIS against existing benchmarks.

翻译：标准罕见事件模拟技术需要精确的分布设定，这在存在分布不确定性时限制了其有效性。为解决这一问题，我们开发了一种新颖的框架，用于估计在此类分布模型风险下的罕见事件概率。具体而言，我们专注于计算最坏情况罕见事件概率，该概率被定义为针对以特定名义分布为中心的Wasserstein模糊集的分布鲁棒性界。通过利用该界的对偶表征，我们提出了分布鲁棒重要性采样（DRIS），这是一种计算上易于处理的方法，旨在显著降低与估计对偶分量相关的方差。所提方法实现简单且采样成本低。最重要的是，它实现了相对误差趋近于零，这是罕见事件模拟中极难建立的最强效率保证。我们的数值研究证实了DRIS相对于现有基准方法的优越性能。