Abstract

We study stress-scenario generation for systems driven by multivariate heavy-tailed risk factors. Within regions where several losses are simultaneously large, stress analysis concerns both the conditional law of risk factors and the most plausible configurations producing them. We show that both tasks share the same limiting tail law but require distinct, nonnested validity criteria. Tail-measure preservation is necessary and sufficient for first-order validity of joint-stress probabilities and scaled conditional laws; tail-density preservation governs likelihood-based reverse stress testing. We develop SSGEN (Self-Similar Generative Estimation), a data-driven input model that exploits the polar decomposition of extremes by learning the angular law from intermediate exceedances and extrapolating radially through a Pareto law. We prove that SSGEN satisfies both criteria and derive convergence rates for the generated stressed law and reverse-stress solutions even without target-event observations. These guarantees transfer to decision problems based on stress-conditioned laws or likelihood-defined stress regions: optimal values and, under uniqueness, solutions converge.