Paper: arXiv 2601.01642

Authors: Dohyun Ahn, Huiyi Chen, Lewen Zheng

Abstract

Standard rare-event simulation techniques require exact distributional specifications, which limits their effectiveness in the presence of distributional uncertainty. To address this, we develop a novel framework for estimating rare-event probabilities subject to such distributional model risk. Specifically, we focus on computing worst-case rare-event probabilities, defined as a distributionally robust bound against a Wasserstein ambiguity set centered at a specific nominal distribution. By exploiting a dual characterization of this bound, we propose Distributionally Robust Importance Sampling (DRIS), a computationally tractable methodology designed to substantially reduce the variance associated with estimating the dual components. The proposed method is simple to implement and requires low sampling costs. Most importantly, it achieves vanishing relative error, the strongest efficiency guarantee that is notoriously difficult to establish in rare-event simulation. Our numerical studies confirm the superior performance of DRIS against existing benchmarks.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper is mathematically dense, featuring advanced theoretical constructs such as Wasserstein metrics, dual reformulations, Vapnik-Chervonenkis empirical process theory, and a vanishing relative error guarantee. However, the provided summary focuses on theoretical novelty and general numerical studies rather than specific backtest protocols, high-frequency data handling, or executable code, placing it firmly in theoretical research.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Estimate rare-event probabilities<br>under distributional uncertainty"] --> B["Methodology:<br>Distributionally Robust Optimization<br>Wasserstein Ambiguity Set"]
  B --> C["Key Framework:<br>Dual Characterization<br>of Worst-Case Bound"]
  C --> D["Proposed Method:<br>Distributionally Robust<br>Importance Sampling DRIS"]
  D --> E["Computational Process:<br>Minimize Variance of<br>Dual Component Estimates"]
  E --> F["Key Finding:<br>Achieves Vanishing Relative Error<br>(Optimal Efficiency)"]
  F --> G["Outcome:<br>Low Sampling Cost &<br>Superior Performance vs. Benchmarks"]

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  439. Options on the Minimum or the Maximum of Two Risky Assets: Analysis and Applications (1982)
  440. Options on the Maximum or the Minimum of Several Assets (1987)
  441. Numerical Evaluation of Multivariate Contingent Claims (1989)
  442. Option Pricing: A Simplified Approach (1979)
  443. Importance Sampling for the Simulation of Highly Reliable Markovian Systems (1994)
  444. Counterexamples in Importance Sampling for Large Deviations Probabilities (1997)
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  466. The Cross-Entropy Method: A Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation, and Machine Learning (2004)
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  482. Optimal I mportance- S ampling D ensity E stimator (1992)
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  510. Some Characterizations of the Multivariate t Distribution (1972)
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  515. Semiparametric Cross Entropy for Rare-Event Simulation (2016)
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