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<p>Distortion risk measures are important tools for quantifying downside risk under uncertainty. Their accurate estimation becomes challenging when the underlying loss variable is generated by a computationally expensive simulation model without analytical tractability. In this paper, we develop an importance sampling method for the efficient Monte Carlo estimation of distortion risk measures in such black-box models. The method combines importance sampling with machine learning approximations in order to reduce computational cost. Its performance is illustrated in numerical experiments for several distortion risk measures and simulation models.</p>

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An integrated approach to importance sampling and machine learning for efficient Monte Carlo estimation of distortion risk measures in black-box models

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年7月8日

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  • Sören Bettels,
  • Stefan Weber

摘要

Distortion risk measures are important tools for quantifying downside risk under uncertainty. Their accurate estimation becomes challenging when the underlying loss variable is generated by a computationally expensive simulation model without analytical tractability. In this paper, we develop an importance sampling method for the efficient Monte Carlo estimation of distortion risk measures in such black-box models. The method combines importance sampling with machine learning approximations in order to reduce computational cost. Its performance is illustrated in numerical experiments for several distortion risk measures and simulation models.