Related papers: Computing Tails of Compound Distributions Using Di…
We propose an analytical approach to the computation of tail probabilities of compound distributions whose individual components have heavy tails. Our approach is based on the contour integration method, and gives rise to a representation…
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…
Recent advancements in Distributional Reinforcement Learning (DRL) for modeling loss distributions have shown promise in developing hedging strategies in derivatives markets. A common approach in DRL involves learning the quantiles of loss…
The estimation of loss distributions for dynamic portfolios requires the simulation of scenarios representing realistic joint dynamics of their components. We propose a novel data-driven approach for simulating realistic, high-dimensional…
Fine-tuning pre-trained diffusion and flow models to optimize downstream utilities is central to real-world deployment. Existing entropy-regularized methods primarily maximize expected reward, providing no mechanism to shape tail behavior.…
We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we…
Conditional Value-at-Risk (CVaR) is a widely used risk metric in applications such as finance. We derive concentration bounds for CVaR estimates, considering separately the cases of light-tailed and heavy-tailed distributions. In the…
We present a flexible, deterministic numerical method for computing left-tail rare events of sums of non-negative, independent random variables. The method is based on iterative numerical integration of linear convolutions by means of…
Extending Buehler et al.'s 2019 Deep Hedging paradigm, we innovatively employ deep neural networks to parameterize convex-risk minimization (CVaR/ES) for the portfolio tail-risk hedging problem. Through comprehensive numerical experiments…
Several novel statistical methods have been developed to estimate large integrated volatility matrices based on high-frequency financial data. To investigate their asymptotic behaviors, they require a sub-Gaussian or finite high-order…
Conditional value-at-risk (CVaR) and value-at-risk (VaR) are popular tail-risk measures in finance and insurance industries as well as in highly reliable, safety-critical uncertain environments where often the underlying probability…
This paper proposes a Mixture Density Network specifically designed for forecasting time series that exhibit locally explosive behavior. By incorporating skewed t-distributions as mixture components, our approach offers enhanced flexibility…
The error scaling for Markov-Chain Monte Carlo techniques (MCMC) with $N$ samples behaves like $1/\sqrt{N}$. This scaling makes it often very time intensive to reduce the error of computed observables, in particular for applications in…
In this work, we introduce a control variate approximation technique for low error approximate Deep Neural Network (DNN) accelerators. The control variate technique is used in Monte Carlo methods to achieve variance reduction. Our approach…
High-dimensional covariance estimation is notoriously sensitive to outliers. While statistically optimal estimators exist for general heavy-tailed distributions, they often rely on computationally expensive techniques like semidefinite…
In a number of applications, particularly in financial and actuarial mathematics, it is of interest to characterize the tail distribution of a random variable $V$ satisfying the distributional equation $V\stackrel{\mathcal{D}}{=}f(V)$,…
Trajectory prediction methods have been widely applied in autonomous driving technologies. Although the overall performance accuracy of trajectory prediction is relatively high, the lack of trajectory data in critical scenarios in the…
In this paper we consider the problem of computing tail probabilities of the distribution of a random sum of positive random variables. We assume that the individual variables follow a reproducible natural exponential family (NEF)…
Ensuring the safety of neural networks under input uncertainty is a fundamental challenge in safety-critical applications. This paper builds on and expands Fazlyab's quadratic-constraint (QC) and semidefinite-programming (SDP) framework for…
This paper develops and estimates a multivariate affine GARCH(1,1) model with Normal Inverse Gaussian innovations that captures time-varying volatility, heavy tails, and dynamic correlation across asset returns. We generalize the…