We consider multi-step algorithms for the computation of the historical expected shortfall. At each step of the algorithms, we use Monte Carlo simulations to reduce the number of historical scenarios that potentially belong to the set of worst-case scenarios. We show how this can be optimized by either solving a simple deterministic dynamic programming algorithm or in an adaptive way by using a stochastic dynamic programming procedure under a given prior. We prove ${\mathbb{L}}^p$-error bounds and numerical tests are performed.

中文翻译：

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通过快速检测最坏情况计算预期短缺

我们考虑使用多步算法来计算历史预期缺口。在算法的每个步骤中，我们使用蒙特卡罗模拟来减少可能属于最坏情况集合的历史场景的数量。我们展示了如何通过解决简单的确定性动态规划算法或通过在给定先验下使用随机动态规划过程以自适应方式优化这一点。我们证明${\mathbb{升}}^{磷}$- 执行错误界限和数值测试。