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This volume is a collection of six papers on the use of auxiliary information and 'a priori' values in construction of improved estimators. The work included here will be of immense application for researchers and students who emply…

Methodology · Statistics 2010-02-19 Rajesh Singh , Pankaj Chauhan , Nirmala Sawan , Florentin Smarandache

We study risk-sensitive Reinforcement Learning (RL), where we aim to maximize the Conditional Value at Risk (CVaR) with a fixed risk tolerance $\tau$. Prior theoretical work studying risk-sensitive RL focuses on the tabular Markov Decision…

Machine Learning · Computer Science 2023-11-21 Yulai Zhao , Wenhao Zhan , Xiaoyan Hu , Ho-fung Leung , Farzan Farnia , Wen Sun , Jason D. Lee

We address the problem that classical risk measures may not detect the tail risk adequately. This can occur for instance due to averaging when calculating the Expected Shortfall. The current literature proposes the so-called adjusted…

Mathematical Finance · Quantitative Finance 2025-04-24 Jascha Alexander , Christian Laudagé , Jörn Sass

The extreme cases of risk measures, when considered within the context of distributional ambiguity, provide significant guidance for practitioners specializing in risk management of quantitative finance and insurance. In contrast to the…

Risk Management · Quantitative Finance 2025-07-01 Yuting Su , Taizhong Hu , Zhenfeng Zou

Handling nominal covariates with a large number of categories is challenging for both statistical and machine learning techniques. This problem is further exacerbated when the nominal variable has a hierarchical structure. We commonly rely…

Methodology · Statistics 2024-06-13 Bavo D. C. Campo , Katrien Antonio

CoVaR (conditional value-at-risk) is a crucial measure for assessing financial systemic risk, which is defined as a conditional quantile of a random variable, conditioned on other random variables reaching specific quantiles. It enables the…

Risk Management · Quantitative Finance 2023-10-31 Weihuan Huang

Odds ratios obtained from logistic models fail to approximate risk ratios with common outcomes, leading to potential misinterpretations about exposure effects by practitioners. This article investigates the complementary log-log models as a…

Methodology · Statistics 2025-06-03 Yuji Tsubota , Kenji Beppu

Markov decision processes are widely used for planning and verification in settings that combine controllable or adversarial choices with probabilistic behaviour. The standard analysis algorithm, value iteration, only provides a lower bound…

Logic in Computer Science · Computer Science 2019-10-21 Arnd Hartmanns , Benjamin Lucien Kaminski

For many real-world decision-making problems subject to uncertainty, it may be essential to deal with multiple and often conflicting objectives while taking the decision-makers' risk preferences into account. Conditional value-at-risk…

Optimization and Control · Mathematics 2023-02-14 Najmesadat Nazemi , Sophie N. Parragh , Walter J. Gutjahr

The estimation of risk measures recently gained a lot of attention, partly because of the backtesting issues of expected shortfall related to elicitability. In this work we shed a new and fundamental light on optimal estimation procedures…

Risk Management · Quantitative Finance 2017-08-25 Marcin Pitera , Thorsten Schmidt

Risk scores are simple classification models that let users make quick risk predictions by adding and subtracting a few small numbers. These models are widely used in medicine and criminal justice, but are difficult to learn from data…

Machine Learning · Statistics 2020-10-21 Berk Ustun , Cynthia Rudin

We consider economic obstacles that limit the reliability and accuracy of value-at-risk (VaR). Investors who manage large market transactions should take into account the impact of the randomness of large trade volumes on predictions of…

General Economics · Economics 2024-04-30 Victor Olkhov

Algorithmic predictions are increasingly used to inform the allocations of goods and interventions in the public sphere. In these domains, predictions serve as a means to an end. They provide stakeholders with insights into likelihood of…

Computers and Society · Computer Science 2024-05-31 Juan Carlos Perdomo

We study issues of robustness in the context of Quantitative Risk Management and Optimization. We develop a general methodology for determining whether a given risk measurement related optimization problem is robust, which we call…

Risk Management · Quantitative Finance 2021-02-12 Paul Embrechts , Alexander Schied , Ruodu Wang

In an environment of increasingly volatile financial markets, the accurate estimation of risk remains a major challenge. Traditional econometric models, such as GARCH and its variants, are based on assumptions that are often too rigid to…

Artificial Intelligence · Computer Science 2025-08-19 Fredy Pokou , Jules Sadefo Kamdem , François Benhmad

We consider the problem of risk diversification of $\alpha$-stable heavy tailed risks. We study the behaviour of the aggregated Value-at-Risk, with particular reference to the impact of different tail dependence structures on the limits to…

Risk Management · Quantitative Finance 2017-04-25 Umberto Cherubini , Paolo Neri

This paper considers the use for Value-at-Risk computations of the so-called Beta-Kotz distribution based on a general family of distributions including the classical Gaussian model. Actually, this work develops a new method for estimating…

Statistics Theory · Mathematics 2018-06-29 Jean-Michel Loubes , M Andrea Arias-Serna , Francisco Caro-Lopera

We study efficiency improvements in randomized experiments for estimating a vector of potential outcome means using regression adjustment (RA) when there are more than two treatment levels. We show that linear RA which estimates separate…

Econometrics · Economics 2025-01-13 Akanksha Negi , Jeffrey M. Wooldridge

In this paper, we propose the multivariate range Value-at-Risk (MRVaR) and the multivariate range covariance (MRCov) as two risk measures and explore their desirable properties in risk management. In particular, we explain that such…

Statistics Theory · Mathematics 2023-05-17 Baishuai Zuo , Chuancun Yin , Jing Yao

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…

Risk Management · Quantitative Finance 2021-06-21 Anand Deo , Karthyek Murthy