Computation of expected shortfall by fast detection of worst scenarios
提出多步算法，利用蒙特卡洛模拟快速识别最差历史情景，以计算历史预期短缺，并通过确定性或随机动态规划优化，给出误差界和数值测试。
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 Lp-error bounds and numerical tests are performed.