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On monotone completion of risk markets: Limit results for incomplete risk markets
Danny Ralph / Geoffrey Pritchard / Golbon Zakeri / Iman Khajepour
risk managementResource overview

On monotone completion of risk markets: Limit results for incomplete risk markets

Paper2025

by Danny Ralph, Geoffrey Pritchard, Golbon Zakeri, Iman Khajepour

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risk management

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

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  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.

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  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.

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