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<p>We establish epigraphical and uniform laws of large numbers for sample-based approximations of law invariant composite risk functionals. These sample-based approximation schemes include Monte Carlo and certain randomized quasi-Monte Carlo integration methods, such as scrambled net integration. Our results can be applied to the approximation of risk-averse stochastic programs and risk-averse stochastic variational inequalities. Our numerical simulations empirically demonstrate that randomized quasi-Monte Carlo approaches based on scrambled Sobol’ sequences can yield smaller bias and root mean square error than Monte Carlo methods for risk-averse optimization.</p>

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Randomized Quasi-Monte Carlo Methods for Risk-Averse Stochastic Optimization

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月18日

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  • Olena Melnikov,
  • Johannes Milz

摘要

We establish epigraphical and uniform laws of large numbers for sample-based approximations of law invariant composite risk functionals. These sample-based approximation schemes include Monte Carlo and certain randomized quasi-Monte Carlo integration methods, such as scrambled net integration. Our results can be applied to the approximation of risk-averse stochastic programs and risk-averse stochastic variational inequalities. Our numerical simulations empirically demonstrate that randomized quasi-Monte Carlo approaches based on scrambled Sobol’ sequences can yield smaller bias and root mean square error than Monte Carlo methods for risk-averse optimization.