Statistical Learning of Value‐at‐Risk and Expected Shortfall
提出一种非渐近收敛分析方法，用Rademacher界学习条件风险价值和条件预期短缺，适用于重尾金融损失，并通过神经网络回归实现高效学习，在数值实验和金融案例中验证。
ABSTRACT We propose a non‐asymptotic convergence analysis of a two‐step approach to learn a conditional value‐at‐risk (VaR) and a conditional expected shortfall (ES) using Rademacher bounds, in a non‐parametric setup allowing for heavy‐tails on the financial loss. Our approach for the VaR is extended to the problem of learning at once multiple VaRs corresponding to different quantile levels. This results in efficient learning schemes based on neural network quantile and least‐squares regressions. An a posteriori Monte Carlo procedure is introduced to estimate distances to the ground‐truth VaR and ES. This is illustrated by numerical experiments in a Student‐ toy model and a financial case study where the objective is to learn a dynamic initial margin.