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We generalize Quasi-Linear Means by restricting to the tail of the risk distribution and show that this can be a useful quantity in risk management since it comprises in its general form the Value at Risk, the Tail Value at Risk and the…

Risk Management · Quantitative Finance 2025-10-22 Nicole Bäuerle , Tomer Shushi

Financial market forecasting remains a formidable challenge despite the surge in computational capabilities and machine learning advancements. While numerous studies have underscored the precision of computer-generated market predictions,…

Computational Finance · Quantitative Finance 2023-11-16 Reza Yarbakhsh , Mahdieh Soleymani Baghshah , Hamidreza Karimaghaie

We consider an investor, whose portfolio consists of a single risky asset and a risk free asset, who wants to maximize his expected utility of the portfolio subject to managing the Value at Risk (VaR) assuming a heavy tailed distribution of…

Portfolio Management · Quantitative Finance 2020-12-02 Subhojit Biswas , Mrinal K. Ghosh , Diganta Mukherjee

Inference over tails is usually performed by fitting an appropriate limiting distribution over observations that exceed a fixed threshold. However, the choice of such threshold is critical and can affect the inferential results. Extreme…

Statistical Finance · Quantitative Finance 2019-02-26 Chiara Lattanzi , Manuele Leonelli

Daily ETF risk monitoring can become unreliable when market data quality degrades, market conditions shift, or predictive performance becomes unstable. This paper develops a reliability-aware risk monitoring service for next-day tail-risk…

Risk Management · Quantitative Finance 2026-04-20 Tenghan Zhong , Keyuan Wu

Multivariate regular variation plays a role assessing tail risk in diverse applications such as finance, telecommunications, insurance and environmental science. The classical theory, being based on an asymptotic model, sometimes leads to…

Probability · Mathematics 2011-08-31 Bikramjit Das , Abhimanyu Mitra , Sidney Resnick

This paper attempts to provide a decision-theoretic foundation for the measurement of economic tail risk, which is not only closely related to utility theory but also relevant to statistical model uncertainty. The main result is that the…

Risk Management · Quantitative Finance 2015-08-18 Steven Kou , Xianhua Peng

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…

Machine Learning · Computer Science 2026-04-27 Rico Angell , Raghav Singhal , Zachary Horvitz , Zhou Yu , Rajesh Ranganath , Kathleen McKeown , He He

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…

Machine Learning · Computer Science 2021-06-23 Shubhada Agrawal , Wouter M. Koolen , Sandeep Juneja

Risk measures, which typically evaluate the impact of extreme losses, are highly sensitive to misspecification in the tails. This paper studies a robust optimization approach to combat tail uncertainty by proposing a unifying framework to…

Optimization and Control · Mathematics 2024-12-09 Guanyu Jin , Roger J. A. Laeven , Dick den Hertog , Aharon Ben-Tal

Value at risk (VaR) and expected shortfall (ES) are common high quantile-based risk measures adopted in financial regulations and risk management. In this paper, we propose a tail risk measure based on the most probable maximum size of risk…

Risk Management · Quantitative Finance 2025-06-17 Kan Chen , Tuoyuan Cheng

Machine learning models are increasingly used in a wide variety of financial settings. The difficulty of understanding the inner workings of these systems, combined with their wide applicability, has the potential to lead to significant new…

Computational Finance · Quantitative Finance 2021-02-10 Samuel N. Cohen , Derek Snow , Lukasz Szpruch

Sophisticated machine learning (ML) models to inform trading in the financial sector create problems of interpretability and risk management. Seemingly robust forecasting models may behave erroneously in out of distribution settings. In…

Machine Learning · Computer Science 2021-10-01 Gabriel Deza , Adelin Travers , Colin Rowat , Nicolas Papernot

Long-tailed classification poses a challenge due to its heavy imbalance in class probabilities and tail-sensitivity risks with asymmetric misprediction costs. Recent attempts have used re-balancing loss and ensemble methods, but they are…

Machine Learning · Computer Science 2023-03-22 Bolian Li , Ruqi Zhang

This paper measures and compares the tail risks of limit and market orders using Extreme Value Theory. The analysis examines realised tail outcomes using the Dealing 2000-2 electronic broking system based on completed transactions rather…

Statistical Finance · Quantitative Finance 2011-03-30 john cotter , kevin dowd

In finance, sequential decision problems are often faced, for which reinforcement learning (RL) emerges as a promising tool for optimisation without the need of analytical tractability. However, the objective of classical RL is the expected…

Computational Finance · Quantitative Finance 2026-02-13 Federico Cacciamani , Roberto Daluiso , Marco Pinciroli , Michele Trapletti , Edoardo Vittori

Long-tail motion forecasting is a core challenge for autonomous driving, where rare yet safety-critical events-such as abrupt maneuvers and dense multi-agent interactions-dominate real-world risk. Existing approaches struggle in these…

Computational Engineering, Finance, and Science · Computer Science 2025-11-11 Bin Rao , Chengyue Wang , Haicheng Liao , Qianfang Wang , Yanchen Guan , Jiaxun Zhang , Xingcheng Liu , Meixin Zhu , Kanye Ye Wang , Zhenning Li

The masses of data now available have opened up the prospect of discovering weak signals using machine-learning algorithms, with a view to predictive or interpretation tasks. As this survey of recent results attempts to show, bringing…

Statistics Theory · Mathematics 2026-05-06 Stephan Clémençon , Anne Sabourin

With the fast development of quantitative portfolio optimization in financial engineering, lots of AI-based algorithmic trading strategies have demonstrated promising results, among which reinforcement learning begins to manifest…

Mathematical Finance · Quantitative Finance 2023-03-10 Huifang Huang , Ting Gao , Pengbo Li , Jin Guo , Peng Zhang , Nan Du

A diversified risk-adjusted time-series momentum (TSMOM) portfolio can deliver substantial abnormal returns and offer some degree of tail risk protection during extreme market events. The performance of existing TSMOM strategies, however,…

Computational Finance · Quantitative Finance 2023-06-29 Joel Ong , Dorien Herremans