Computation of expected shortfall by fast detection of worst scenarios

Bruno Bouchard, Adil Reghai and Benjamin Virrion

Quantitative Finance, 2021, vol. 21, issue 7, 1087-1108

Abstract: 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} $Lp-error bounds and numerical tests are performed.

Date: 2021
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DOI: 10.1080/14697688.2021.1880618

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