Financial Tail Risk Beyond Lipschitz Continuity via Semi-Discrete Optimal Transport
Read the original on arXiv Statistics ML →The Flow has not summarised this story yet — read it at arXiv Statistics ML.
The Flow has not summarised this story yet — read it at arXiv Statistics ML.
arXiv:2608. 11544v1 Announce Type: cross Abstract: We propose CVaR-penalized Generative Particle Algorithm (CVaR-GPA), a robust, tail-agnostic algorithm for fine-tuning generative models to learn heavy-tailed distributions and capture extreme events, requiring no prior knowledge or estimation of the target's tail characteristics.
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The paper introduces a penalized distributionally robust optimization framework that allows an adversary to choose any distribution while incurring a Wasserstein penalty for deviating from the empirical distribution. It shows that the adversary’s problem can be reformulated as optimizing transport maps that push empirical samples to adversarial ones, proving that optimal maps are cyclically monotone. The authors argue that standard per-sample adversarial training violates this property and propose two remedies—multi-start particle ascent and input-convex neural network parameterization—to enforce cyclical monotonicity, demonstrating improved robustness and generalization in experiments on regression, image classification, and control tasks.
arXiv:2607. 13841v1 Announce Type: new Abstract: Heavy-tailed data arise in many domains where rare events carry disproportionate importance, such as imbalanced image datasets, financial returns, and weather extremes.