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Financial Tail Risk Beyond Lipschitz Continuity via Semi-Discrete Optimal Transport
Kibaek Lee / Namid Stillman / Ryan M. Engel
machine learning / portfolio optimizationResource overview

Financial Tail Risk Beyond Lipschitz Continuity via Semi-Discrete Optimal Transport

Paper2026

by Kibaek Lee, Namid Stillman, Ryan M. Engel

Tags
machine learningportfolio optimizationrisk managementtail risk

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Understand this paper

Suggested foundations for risk measurement and stress and portfolio construction. Specialist prerequisites vary by paper.

Before you read

  1. Random Variables and Distributions

    Represent losses as a distribution rather than one forecast.

  2. Expected Shortfall and Other Tail Risk Measures

    Distinguish a loss quantile from the average loss in the tail.

  3. Eigenvalues and Covariance Matrices

    Understand the covariance structure of portfolio risk.

  4. Constrained and Convex Optimisation

    Read objectives, constraints and optimality conditions.

Go further

  1. VaR Estimation in Practice: Variance-Covariance, Historical Simulation, Monte Carlo

    Compare risk estimators and their assumptions.

  2. Backtesting VaR and ES: Coverage Tests and Model Validation

    Check forecasts against realised losses.

  3. Mean-Variance Optimisation

    Construct allocations and examine sensitivity to estimated inputs.

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