# Statistical Learning of Value-at-Risk and Expected Shortfall

arXiv: https://arxiv.org/abs/2209.06476 · HTML: https://mlsanity.com/paper/2209.06476/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 40 references that are in the map.
- First posted on arXiv 14 Sep 2022.

## Builds on (most cited first, 5 of 5)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Size-Independent Sample Complexity of Neural Networks](https://mlsanity.com/paper/1712.06541/) (2017)
- [Beyond expectation: Deep joint mean and quantile regression for spatio-temporal problems](https://mlsanity.com/paper/1808.08798/) (2018)
- [Quantile regression with deep ReLU Networks: Estimators and minimax rates](https://mlsanity.com/paper/2010.08236/) (2020)
- [Smooth Pinball Neural Network for Probabilistic Forecasting of Wind Power](https://mlsanity.com/paper/1710.01720/) (2017)

## Built on by (most cited first, 1 of 1)

- [An Explicit Scheme for Pathwise XVA Computations](https://mlsanity.com/paper/2401.13314/) (2024)

## Abstract (arXiv)

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-t toy model and a financial case study where the objective is to learn a dynamic initial margin.