Paper: arXiv 2510.18995

Authors: Alexandre Boumezoued, Adel Cherchali, Vincent Lemaire, Gilles Pagès, Mathieu Truc

Abstract

Estimating risk measures such as large loss probabilities and Value-at-Risk is fundamental in financial risk management and often relies on computationally intensive nested Monte Carlo methods. While Multi-Level Monte Carlo (MLMC) techniques and their weighted variants are typically more efficient, their effectiveness tends to deteriorate when dealing with irregular functions, notably indicator functions, which are intrinsic to these risk measures. We address this issue by introducing a novel MLMC parametrization that significantly improves performance in practical, non-asymptotic settings while maintaining theoretical asymptotic guarantees. We also prove that antithetic sampling of MLMC levels enhances efficiency regardless of the regularity of the underlying function. Numerical experiments motivated by the calculation of economic capital in a life insurance context confirm the practical value of our approach for estimating loss probabilities and quantiles, bridging theoretical advances and practical requirements in financial risk estimation.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper is densely mathematical with advanced probability theory, measure theory, and theoretical proofs for MLMC optimization and antithetic sampling, while the empirical section is described conceptually without showing specific code, datasets, or backtest results.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Efficient Risk Measure Estimation<br>Value-at-Risk / Loss Probabilities"] --> B["Data Inputs & Assumptions:<br>Nested Simulations<br>Financial/Life Insurance Models"]
  B --> C["Key Methodology:<br>1. Optimized MLMC Parametrization<br>2. Antithetic Sampling"]
  C --> D["Computational Processes:<br>Adaptive Level Allocation<br>Correlated Sampling"]
  D --> E["Outcomes & Findings:<br>• Improved Efficiency for Irregular Functions<br>• Guaranteed Asymptotic Convergence<br>• Practical Application in Economic Capital"]

Cited References (41)

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and 33 more
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2 of 41 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.