arXiv subjects

Mantu Gupta

Publications and source records attributed to Mantu Gupta.

2 recordsLinked to original sources

arXiv2026

Simulating Stress Laws under Extremal Dependence: Characterizing What Generative Models Must Preserve

We study stress-scenario generation for systems driven by multivariate heavy-tailed risk factors. Within regions where several financial losses are simultaneously extreme, stress analysis concerns both the conditional law of the risk factors and the most plausible configurations producing those losses. We show that both are governed by the same limiting tail law. Preserving its measure recovers rare-event probabilities and scaled conditional stress laws, while misspecifying extremal dependence distorts some regular joint-stress probability. Its density governs reverse-stress optimization, whose maximizers identify the most plausible stress configurations. To exploit this common structure in finite samples, we develop SSGEN (Self-Similar Generative Estimation), which learns extremal dependence from intermediate exceedances and extrapolates to rarer levels using a Pareto radial component. Even when the target event is absent from the sample, we establish convergence rates for the generated conditional law, and data-driven reverse-stress solutions.

q-fin.RM↗

arXiv2026

An Extreme Value Perspective on Learning Stress Laws

We introduce Self-Similar Generative Estimation (SS-GEN), a method for simulating multivariate tail events and estimating rare-event probabilities in both heavy and light-tailed settings. SS-GEN exploits asymptotic tail structure to decompose the tail distribution into an explicit radial component and a nonparametric angular component, reducing tail learning to a compact-domain problem that can be handled by off-the-shelf deep generative models. The resulting sampler generates representative extreme scenarios and supports probability estimation far beyond the observed data. Under mild nonparametric tail assumptions, we show that the SS-GEN density is asymptotically exact in the tail, with vanishing uniform relative error for regularly varying distributions and vanishing uniform log-relative error for Weibull-type distributions. Unlike existing approaches that rely on specialized architectures or parametric tail specifications, SS-GEN leverages asymptotic tail structure to enable standard generative models to generate representative extreme samples and estimate rare-event probabilities beyond the observed data.

q-fin.RM↗