arXiv subjects

Anand Deo

Publications and source records attributed to Anand Deo.

15 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

No Unique Minimizer, No Problem: On the Consistency of Robust Neural Classifiers

Neural network classifiers trained by cross-entropy minimization are highly sensitive to label noise and adversarial contamination. While robust alternatives offer bounded influence and resistance to corruption, their statistical foundations in the deep learning setting are insufficient due to a fundamental difficulty: neural parameterizations are non-identifiable, so the population loss minimizer is an equivalence class of parameters, not a unique point. We develop a consistency theory for robust neural classifiers based on the S-divergence family that requires no identifiability assumption. Casting training as stochastic optimization over a non-identifiable parameter space, we prove that empirical S-divergence minimizers converge to the population-optimal equivalence class under mild regularity conditions, and verify these conditions for three architecture choices. We further establish that limit points of the robust training algorithm are stationary points of the empirical objective. Experiments on vision and language benchmark datasets confirm that S-divergence training maintains clean-data accuracy while exhibiting performance competitive with existing robust methods.

cs.LG↗

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↗

arXiv2026

Generating Plausible Stress Scenarios via Large Deviations

Financial stress tests based on handpicked scenarios can mislead risk management by overlooking genuinely dangerous configurations or overemphasising shocks that are too implausible to be decision-relevant. We develop a systematic method for generating plausible stress scenarios for financial losses driven by exogenous risk factors. The method exploits a large-deviations principle: conditional on a large loss, the risk factors concentrate near the most likely stress configurations. We use this structure to define representative stress distributions and to extrapolate observed samples into more extreme scenarios while preserving the relative plausibility of stress mechanisms. As a result, the procedure can generate informative stress scenarios even when historical data contain few or no observations in the stressed regime. Numerical experiments on two financial network models show that the method recovers the stressed loss law and key stress diagnostics, including in settings where benchmark generators fail to generate any stressed samples.

q-fin.RM↗

arXiv2026

Decision-Scaled Scenario Approach for Rare Chance-Constrained Optimization

Chance-constrained optimization is a suitable modeling framework for safety-critical applications where violating constraints is nearly unacceptable. The scenario approach is a popular solution method for these problems, due to its straightforward implementation and ability to preserve problem structure. However, in the rare-event regime where constraint violations must be kept extremely unlikely, the scenario approach becomes computationally infeasible due to the excessively large sample sizes it demands. We address this limitation with a new yet straightforward decision-scaling method that relies exclusively on original data samples and a single scalar hyperparameter that scales the constraints in a way amenable to standard solvers. Our method leverages large deviation principles under mild nonparametric assumptions satisfied by commonly used distribution families in practice. For a broad class of problems satisfying certain practically verifiable structural assumptions, the method achieves a polynomial reduction in sample size requirements compared to the classical scenario approach, while also guaranteeing asymptotic feasibility in the rare-event regime. Numerical experiments spanning finance and engineering applications show that our decision-scaling method significantly expands the scope of problems that can be solved both efficiently and reliably.

math.OC↗

arXiv2025

EVT-Based Rate-Preserving Distributional Robustness for Tail Risk Functionals

Risk measures such as Conditional Value-at-Risk (CVaR) focus on extreme losses, where scarce tail data makes model error unavoidable. To hedge misspecification, one evaluates worst-case tail risk over an ambiguity set. Using Extreme Value Theory (EVT), we derive first-order asymptotics for worst-case tail risk for a broad class of tail-risk measures under standard ambiguity sets, including Wasserstein balls and $\phi$-divergence neighborhoods. We show that robustification can alter the nominal tail asymptotic scaling as the tail level $\beta\to0$, leading to excess risk inflation. Motivated by this diagnostic, we propose a tail-calibrated ambiguity design that preserves the nominal tail asymptotic scaling while still guarding against misspecification. Under standard domain of attraction assumptions, we prove that the resulting worst-case risk preserves the baseline first-order scaling as $\beta\to0$, uniformly over key tuning parameters, and that a plug-in implementation based on consistent tail-index estimation inherits these guarantees. Synthetic and real-data experiments show that the proposed design avoids the severe inflation often induced by standard ambiguity sets.

q-fin.RM↗

arXiv2025

The Scaling Behaviors in Achieving High Reliability via Chance-Constrained Optimization

We study the problem of resource provisioning under stringent reliability or service level requirements, which arise in applications such as power distribution, emergency response, cloud server provisioning, and regulatory risk management. With chance-constrained optimization serving as a natural starting point for modeling this class of problems, our primary contribution is to characterize how the optimal costs and decisions scale for a generic joint chance-constrained model as the target probability of satisfying the service/reliability constraints approaches its maximal level. Beyond providing insights into the behavior of optimal solutions, our scaling framework has three key algorithmic implications. First, in distributionally robust optimization (DRO) modeling of chance constraints, we show that widely used approaches based on KL-divergences, Wasserstein distances, and moments heavily distort the scaling properties of optimal decisions, leading to exponentially higher costs. In contrast, incorporating marginal distributions or using appropriately chosen f-divergence balls preserves the correct scaling, ensuring decisions remain conservative by at most a constant or logarithmic factor. Second, we leverage the scaling framework to quantify the conservativeness of common inner approximations and propose a simple line search to refine their solutions, yielding near-optimal decisions. Finally, given N data samples, we demonstrate how the scaling framework enables the estimation of approximately Pareto-optimal decisions with constraint violation probabilities significantly smaller than the Omega(1/N)-barrier that arises in the absence of parametric assumptions

math.OC↗

arXiv2024

Reduced Sample Complexity in Scenario-Based Control System Design via Constraint Scaling

The scenario approach is widely used in robust control system design and chance-constrained optimization, maintaining convexity without requiring assumptions about the probability distribution of uncertain parameters. However, the approach can demand large sample sizes, making it intractable for safety-critical applications that require very low levels of constraint violation. To address this challenge, we propose a novel yet simple constraint scaling method, inspired by large deviations theory. Under mild nonparametric conditions on the underlying probability distribution, we show that our method yields an exponential reduction in sample size requirements for bilinear constraints with low violation levels compared to the classical approach, thereby significantly improving computational tractability. Numerical experiments on robust pole assignment problems support our theoretical findings.

math.OC↗

arXiv2023

Importance Sampling for Minimization of Tail Risks: A Tutorial

This paper provides an introductory overview of how one may employ importance sampling effectively as a tool for solving stochastic optimization formulations incorporating tail risk measures such as Conditional Value-at-Risk. Approximating the tail risk measure by its sample average approximation, while appealing due to its simplicity and universality in use, requires a large number of samples to be able to arrive at risk-minimizing decisions with high confidence. This is primarily due to the rarity with which the relevant tail events get observed in the samples. In simulation, Importance Sampling is among the most prominent methods for substantially reducing the sample requirement while estimating probabilities of rare events. Can importance sampling be used for optimization as well? If so, what are the ingredients required for making importance sampling an effective tool for optimization formulations involving rare events? This tutorial aims to provide an introductory overview of the two key ingredients in this regard, namely, (i) how one may arrive at an importance sampling change of measure prescription at every decision, and (ii) the prominent techniques available for integrating such a prescription within a solution paradigm for stochastic optimization formulations.

q-fin.RM↗

arXiv2023

Achieving Efficiency in Black Box Simulation of Distribution Tails with Self-structuring Importance Samplers

This paper presents a novel Importance Sampling (IS) scheme for estimating distribution tails of performance measures modeled with a rich set of tools such as linear programs, integer linear programs, piecewise linear/quadratic objectives, feature maps specified with deep neural networks, etc. The conventional approach of explicitly identifying efficient changes of measure suffers from feasibility and scalability concerns beyond highly stylized models, due to their need to be tailored intricately to the objective and the underlying probability distribution. This bottleneck is overcome in the proposed scheme with an elementary transformation which is capable of implicitly inducing an effective IS distribution in a variety of models by replicating the concentration properties observed in less rare samples. This novel approach is guided by developing a large deviations principle that brings out the phenomenon of self-similarity of optimal IS distributions. The proposed sampler is the first to attain asymptotically optimal variance reduction across a spectrum of multivariate distributions despite being oblivious to the specifics of the underlying model. Its applicability is illustrated with contextual shortest path and portfolio credit risk models informed by neural networks

stat.ML↗

arXiv2022

Combining Retrospective Approximation with Importance Sampling for Optimising Conditional Value at Risk

This paper investigates the use of retrospective approximation solution paradigm in solving risk-averse optimization problems effectively via importance sampling (IS). While IS serves as a prominent means for tackling the large sample requirements in estimating tail risk measures such as Conditional Value at Risk (CVaR), its use in optimization problems driven by CVaR is complicated by the need to tailor the IS change of measure differently to different optimization iterates and the circularity which arises as a consequence. The proposed algorithm overcomes these challenges by employing a univariate IS transformation offering uniform variance reduction in a retrospective approximation procedure well-suited for tuning the IS parameter choice. The resulting simulation based approximation scheme enjoys both the computational efficiency bestowed by retrospective approximation and logarithmically efficient variance reduction offered by importance sampling

q-fin.RM↗

arXiv2021

Efficient Black-Box Importance Sampling for VaR and CVaR Estimation

This paper considers Importance Sampling (IS) for the estimation of tail risks of a loss defined in terms of a sophisticated object such as a machine learning feature map or a mixed integer linear optimisation formulation. Assuming only black-box access to the loss and the distribution of the underlying random vector, the paper presents an efficient IS algorithm for estimating the Value at Risk and Conditional Value at Risk. The key challenge in any IS procedure, namely, identifying an appropriate change-of-measure, is automated with a self-structuring IS transformation that learns and replicates the concentration properties of the conditional excess from less rare samples. The resulting estimators enjoy asymptotically optimal variance reduction when viewed in the logarithmic scale. Simulation experiments highlight the efficacy and practicality of the proposed scheme

q-fin.RM↗

arXiv2020

Optimizing tail risks using an importance sampling based extrapolation for heavy-tailed objectives

Motivated by the prominence of Conditional Value-at-Risk (CVaR) as a measure for tail risk in settings affected by uncertainty, we develop a new formula for approximating CVaR based optimization objectives and their gradients from limited samples. A key difficulty that limits the widespread practical use of these optimization formulations is the large amount of data required by the state-of-the-art sample average approximation schemes to approximate the CVaR objective with high fidelity. Unlike the state-of-the-art sample average approximations which require impractically large amounts of data in tail probability regions, the proposed approximation scheme exploits the self-similarity of heavy-tailed distributions to extrapolate data from suitable lower quantiles. The resulting approximations are shown to be statistically consistent and are amenable for optimization by means of conventional gradient descent. The approximation is guided by means of a systematic importance-sampling scheme whose asymptotic variance reduction properties are rigorously examined. Numerical experiments demonstrate the superiority of the proposed approximations and the ease of implementation points to the versatility of settings to which the approximation scheme can be applied.

stat.ME↗

arXiv2020

City-Scale Agent-Based Simulators for the Study of Non-Pharmaceutical Interventions in the Context of the COVID-19 Epidemic

We highlight the usefulness of city-scale agent-based simulators in studying various non-pharmaceutical interventions to manage an evolving pandemic. We ground our studies in the context of the COVID-19 pandemic and demonstrate the power of the simulator via several exploratory case studies in two metropolises, Bengaluru and Mumbai. Such tools become common-place in any city administration's tool kit in our march towards digital health.

q-bio.PE↗

arXiv2019

Credit Risk: Simple Closed Form Approximate Maximum Likelihood Estimator

We consider discrete default intensity based and logit type reduced form models for conditional default probabilities for corporate loans where we develop simple closed form approximations to the maximum likelihood estimator (MLE) when the underlying covariates follow a stationary Gaussian process. In a practically reasonable asymptotic regime where the default probabilities are small, say 1-3% annually, the number of firms and the time period of data available is reasonably large, we rigorously show that the proposed estimator behaves similarly or slightly worse than the MLE when the underlying model is correctly specified. For more realistic case of model misspecification, both estimators are seen to be equally good, or equally bad. Further, beyond a point, both are more-or-less insensitive to increase in data. These conclusions are validated on empirical and simulated data. The proposed approximations should also have applications outside finance, where logit-type models are used and probabilities of interest are small.

econ.EM↗