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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…
Computation of extreme quantiles and tail-based risk measures using standard Monte Carlo simulation can be inefficient. A method to speed up computations is provided by importance sampling. We show that importance sampling algorithms,…
In this paper, we consider a simple estimator for tail dependence coefficients of a max-stable time series and show its asymptotic normality under a mild condition. The novelty of our result is that this condition does not involve mixing…
The extreme values theory presents specific tools for modeling and predicting extreme phenomena. In particular, risk assessment is often analyzed through measures for tail dependence and high values clustering. Despite technological…
Maximum Likelihood Estimation (MLE) and Likelihood Ratio Test (LRT) are widely used methods for estimating the transition probability matrix in Markov chains and identifying significant relationships between transitions, such as equality.…
We propose and analyze TRAiL (Tangential Randomization in Linear Bandits), a computationally efficient regret-optimal forced exploration algorithm for linear bandits on action sets that are sublevel sets of strongly convex functions. TRAiL…
Assessing the probability of occurrence of extreme events is a crucial issue in various fields like finance, insurance, telecommunication or environmental sciences. In a multivariate framework, the tail dependence is characterized by the…
In risk management, tail risks are of crucial importance. The assessment of risks should be carried out in accordance with the regulatory authority's requirement at high quantiles. In general, the underlying distribution function is…
The paper presents an efficient method for simulating the tails of a target variable Z=h(X) which depends on a set of basic variables X=(X_1, ..., X_n). To this aim, variables X_i, i=1, ..., n are sequentially simulated in such a manner…
Probabilistic forecasts comprehensively describe the uncertainty in the unknown future outcome, making them essential for decision making and risk management. While several methods have been introduced to evaluate probabilistic forecasts,…
Tail Gini functional is a measure of tail risk variability for systemic risks, and has many applications in banking, finance and insurance. Meanwhile, there is growing attention on aymptotic independent pairs in quantitative risk…
Estimating the structures at high or low quantiles has become an important subject and attracted increasing attention across numerous fields. However, due to data sparsity at tails, it usually is a challenging task to obtain reliable…
For a risk vector $V$, whose components are shared among agents by some random mechanism, we obtain asymptotic lower and upper bounds for the individual agents' exposure risk and the aggregated risk in the market. Risk is measured by…
Language models are increasingly capable and are being rapidly deployed on a population-level scale. As a result, the safety of these models is increasingly high-stakes. Fortunately, advances in alignment have significantly reduced the…
Level set estimation (LSE), the problem of identifying the set of input points where a function takes value above (or below) a given threshold, is important in practical applications. When the function is expensive-to-evaluate and…
Based on suitable left-truncated or censored data, two flexible classes of $M$-estimations of Weibull tail coefficient are proposed with two additional parameters bounding the impact of extreme contamination. Asymptotic normality with…
We address the challenge of performing Targeted Maximum Likelihood Estimation (TMLE) after an initial Highly Adaptive Lasso (HAL) fit. Existing approaches that utilize the data-adaptive working model selected by HAL-such as the relaxed HAL…
In several applications, ultimately at the largest data, truncation effects can be observed when analysing tail characteristics of statistical distributions. In some cases truncation effects are forecasted through physical models such as…
In the world of modern financial theory, portfolio construction has traditionally operated under at least one of two central assumptions: the constraints are derived from a utility function and/or the multivariate probability distribution…
This work, based on Random Matrix Theory (RMT), introduces a novel early-stopping strategy for Transformer training dynamics. Utilizing the Power Law (PL) fit to tansformer attention matrices as a probe, we demarcate training into three…